Is it more energy efficient to remove the ballast by using LED Tube?
Summarey:


You MUST use a ballast with an EverLED TR tube.
You should not use a ballast with tubes where the manufacturer says that you should not use a ballast.
If the manufacturer does not make it clear whether you should or should not use a ballast then you should buy another brand of tube. This is such a fundamental issue that all competent manufacturers will address it.




You need to carefully read what EverLED, who you are quoting, say

It is clear from what they say that they are claiming that:


THEIR LED tubes MUST use an external (existing) electromagnetic ballast.
Most other LED tubes that require the external ballast to be removed still need a ballast BUT have it internally. 


In fact, they are speaking rubbish in the second case above. LED tubes can be designed so that they do NOT need have to have a ballast, either external or internal. They do not need a ballast because they work entirely differently to how fluro tubes work.

BUT - just because they are talking rubbish about other people's products, it does not mean that you can  ignore what they say about using their product. It does not matter whetrher the external ballast "wastes" energy - they say you MUST use one with their tubes - leaving it in place may waste energy, but removing it will probably waste the complete $s that you paid for their tube. 

Their FAQ says:


Do you have to remove the ballast when installing the EverLED TR?
No. Unlike other LED replacements for linear fluorescent tubes, the EverLED TR LED Tube Light is the worlds first ballast compatible LED product.
The EverLED-TR is designed to function with both T8 and T12 standard electronic and magnetic ballasts.
This unique feature makes the EverLED-TR a true "drop-in" solution and saves the considerable expense of hiring electricians to rewire the fixture and remove the existing ballast.


and


Is it more energy efficient to remove the ballast?
No, removing the ballast does not make your LED conversion consume less electricity. The ballast is an essential component which converts and regulates power delivered to a fluorescent tube. LEDs also require this power conversion and regulation; it can not be avoided. While it is true that the ballast is not 100% efficient  (nothing is), the LED Tube Lights which require removing the ballast have, simply put, a ballast inside the tube itself. As a result, those products suffer from the exact same inefficiencies as the existing ballast.




Proper use of information:

(1) For most LED fluorescent tube replacements, the manufacturer's instructions probably REQUIRE you to remove the ballast. 

(2) For the example you have given they are DESIGNED to work with the ballast in place. 

SO

(3) You have two examples that are identifiably different, and you cannot extend what it says to the other without taking note of what the manufacturer says in each case.

From what I read on the page that you cited, they are designed to work WITH the ballast BUT I did not see if they say that they NEED the ballast or if it is optional. It is quite possible, but not certain, that removing the ballast in this case would damage the new "tube".  

If the page you had found was about replacing mercury lights, or metal halide lights, or low or high pressure sodium lights, or Xenon arc lights,... with some different sort of lights there would be no reason to think that the advice for one type necessarily applied to all the others. And similarly there is no reason to think so here when there are two types of replacement being talked about.