False copyright claims by "Orchard Music"
Ok, this is quite a complicated problem actually, and depending on the specific situation, the answer might vary. So I'll break this down in a couple of subsections.
CC licences and unauthorized distribution
Creative Commons are a set of licences that allow creators to distribute their original content (e.g. music) using liberal licences under easy to understand terms. However, in order to do so, the uploader needs to hold the rights to the music (usually this means they are the creator). If they don't, they have no right to grant any permissions regarding the use of that music. It's your responsibility to check if they do have those rights.
Excerpt from my answer here:

Remember that just because someone uploads music to a website and claims it's free-to-use, it doesn't mean he actually has the right to do so or the authority to grant you any rights to it. And if you use a copyrighted piece of music in your project without knowing any better, you can stil be held responsible even if you downloaded it from a website that claimed it was free. Always check if the website you are downloading from is legit and if the uploaders actually have to rights to the music (in most cases, that means they made it themselves).

In short, just because someone uploads a Hannah Montana album to some website and puts a CC icon next to it, you still can't use Best of Both Worlds in your video. And if you do, you can't rely on your claim that you got it from that site, because the uploader didn't hold the rights to that music in the first place and it would've been your responsibility to check if they do.
If it's music from a rather unknown author and there were no signs that the original source isn't legit, you might not be held responsible for the 'damage' (claimed by the copyright holder, whether that damage actually exists is a rather philosophical question) caused by your usage of the music. However, even in that case, you'd have to take your video down. So there's no winning in a situation like that.
tl;dr: Always make sure that uploader of whatever music you want to use actually made that music.
In your case, the Soundcloud account looks to be legit, so let's proceed.
CC licenses and retractability
This is only tangetially related to your specific problem, but it's actually something that I think is quite relevant to false copyright claims regarding CC licenced work. All CC licences contain this condition:

The licensor cannot revoke these freedoms as long as you follow the license terms.

What this means is as long as you uphold the terms of the licence, the uploader can't retract the permissions granted by the CC licence. Of course that doesn't mean he has to continue distribution his works indefinetely. But if a music creator at some point decides to stop distributing his work under a CC licence, this doesn't affect any work using his music (e.g. your YouTube video) that was created before that time.
So, assuming you made sure the uploader of the music holds the right to it and follow the licence terms (e.g. proper attribution), your video doesn't infringe any copyright and you are right to dispute such a claim.
(Note: If an artist at some point stops distributing his music under a CC licence, from that point onwards you can't rightfully publish any new work using his music, even if you downloaded it while it was still CC licenced. The non-retractibility only affects works published while the music was being distributed under a CC licence.)
However, being right isn't all there is to it. There's a saying in German:

Recht haben und Recht bekommen sind zwei Paar Schuhe.

Roughly translated: Being right and being proven right are two different things. That's where YouTube's ID system and false copyright claims come into play.
YouTube's ID system

&quot;In the beginning the YouTube ID system was created. This has made a lot of people very angry and been widely regarded as a bad move&quot;

YouTube has a system in place that automatically checks for copyrighted music in uploaded videos and places copyright claims accordingly. The copyright holder of that music (according to YouTube's database) then gets notified and can decide what to do with it; for example, they can have the video taken down, or they can decide to leave it up but receive a portion of this video's ad proceeds. They can also decide on a default action, and that's a big part of the problem that made many people very angry.
In 2013 especially there was much trouble regarding this system. The problem was, the automated ID system was terrible to begin with and would often attribute music wrongly. There were also many scammers that would claim copyright for music that wasn't theirs. The problem is that in cases like this, YouTube favors the copyright holder. So instead of having the person who claims a copyright infringement provide them with proof, the video creator's have to dispute a claim and provide prove that they didn't infringe any copyrights. This usually took a couple of weeks and in the meantime, the person to claim the copyright infringement got all the proceeds from that video.
This system has since been refined and the uproar died down, but you still hear stories like yours occassionaly. When in doubt, YouTube still favors the copyright claimer over the video creator.
The Orchard Group
I hadn't heard of the Orchard Group before, but I've looked through the links you included in your question and did some additional research. As you already said, you are not the first creator to have problems with false copyright claims. On the forums, many people are quick to call them scam artists. But I'm not sure about that. There are also some stories about people that contacted them and got their false copyright claim resolved quickly. I believe the root of the problem might be this:

The Orchard's YouTube multi-channel network has more than 1,000 channels across the globe and uses technology, built in-house, called B.A.C.O.N. (Bulk Automated Claiming on The Orchard Network) to crawl, claim and track YouTube videos to monetize for their clients. It was ranked 7th in the U.S. in July 2014.

Source: Wikipedia
However, according to this source, the Orchard Music isn't unwilling to forfeit wrongly submitted copyright claims:

YouTube users have expressed concerns about The Orchard claiming copyright ownership of music used in user-generated content that may or may not belong to them. According to an article by The Orchard on their Daily Rind blog, if audio is matched to a particular copyright owner via YouTube's content identification system, then one or more links will be placed under the video in order to help promote the copyright owner's music, with the video remaining available. The article states that erroneous claims are removed by The Orchard Team after review upon email communication with their dispute department.
In this context, The Orchard has been criticized by YouTube users for claiming content that is not theirs or in some cases, content that did not exist within the video at all. In a blog post on The Daily Rind, The Orchard explains that this is due to YouTube's automated Content ID matching and outlines steps for resolving this scenario.

So, you got two automated systems that can both screw up and have been shown to do so often. Not an ideal situation for content creators. If you get caught in such an automated system, the solution is almost always to contact the people responsible for it. Contact the Orchard Group and possibly also contact the original artist of the music. If they are indeed not trying to scam anyone, they will be willing to help you. If the Orchard Group doesn't reply, public shaming on Twitter oftentimes helps you get in touch with an actual person, not just with an email autoresponder.
If they actually are scammers or plainly refuse to forfeit their copyright claim, you will have to contact YouTube to get it resolved. So ...
Your questions


How is it possible that Orchard Music can claim ownership of a Creative Commons music production?


As mentioned, this is mostly done by automated systems that are prone to misfires, especially if larger distribution/collection companies are involved. Also, you can claim anything, that doesn't mean you actually have any lawful grounds on which your claim is based. I can claim that I be crowned High King of the Universe, but nobody will have to call me Your Majesty. And if I sue them, I'm unlikely to win that case.


Why do I need a publishing license to a Creative Commons music production?


You don't. The CC licence gives you the right to publish your video if you follow the terms laid out in the licence, you don't need to pay any additional licence fees or royalties. However, a human error is also possible.
For example, maybe the artist is represented by the Orchard Group and never intended to publish their work under a CC licence. Maybe they just forgot to change that setting while uploading their music to Soundcloud. I'm not sure about Soundcloud, but if you for example upload something to Vimeo, a CC-BY licence is applied by default, and you have to go into a submenu of the settings to change that. I think that is a terrible implementation, but that's how it is.
Even if that case, you would probably be within your rights to invoke the licence terms the author published his music under, but it might not be feasible or realistic to do so and see your claim through.


Should I dispute the claim for the second time?


That is your decision. Before you do anything, check if you followed all the licence terms, the legitimacy of your music source and everything else mentioned in this post. It might also be better to contact the Orchard Group or the artist directly to see if you can't get the issue resolved without involving YouTube as a third party. Though a lawyer would probably tell you that contacting them is the worst thing to do if you plan to follow this up with a lawsuit.
Just remember, being right doesn't mean YouTube will take your side. And if they don't, there's little you can do besides suing, which might not be feasible for you.

Disclaimer: I'm not actually sure I answered your question after all that text. I'm sure I forgot something, but there's so many important factors involved, it's hard to put everything into one answer. Feel free to ask if I forgot anything, I'll be happy to edit my answer if I can. Also note that none of this constitutes legal advice. It's rather a description of the current situation regarding YouTube's copyright claims systes and some pointers as to what you can reasonably do to get this problem resolved. Your theoretical (lawful and moral) rights and responsibilites might actually differ from what you can reasonably enforce.