Are altcoins private companies? As far as I have understood, Bitcoin is the Internet of money, using blockchain technology that is open, transnational, neutral, censorship resistant and there is no third-party controlling the network. 

As far as I have also understood, altcoins usually always have founders, they have developer teams, they are basically closed, private, non-neutral, non-censorship resistant networks with a trusted third-party. Please, correct me if I am wrong. 

So, my question is: Are altcoins private companies with private interest to make as much money as possible? Or have I understood something fundamentally wrong? I have tried to Google the answer to this question but I can't find anything. I hope someone could enlighten me a little bit on this issue.
I think you are confusing the monetary function of "coins based on blockchain technology" with the technology itself.  Blockchain technology, and thus any "alt-coin" using that technology, is used to prove the chain of ownership of a some item.  In the case of Bitcoin, that item is money, however it might just as easily be used to prove ownership of oranges.  

Blockchain technology can be used by anyone to create a proof-of-ownership chain.  Therefore, a private company might choose to use it for whatever purpose they desire; that may make it closed, private, non-neutral, and non-censorship resistant.  That doesn't make it wrong, per se.

In the case of "alt coins", always perform due-diligence before making an investment.  Unless a company is designated as "not for profit", practically-speaking the only reason for it to exist is to make money for its owners.