Is there a word that defines the lack of authenticity behind an idea of truth?
Perhaps the word you are looking for is "truthiness".
I'm not sure what is meant by the question but I'll take a stab at it.
Usually we can say that true ideas are solid - that they have as part of their nature authenticity. For instance,
So it's odd to try to look at the lack of authenticity behind an idea of truth. However, if we want to talk about something that someone wants to be true but isn't, a word that was coined in 2005 is truthiness - which, according to the comedian Stephen Colbert who coined it, is "truth that won't stand to be held back by facts". Another way to view it is as an opinion that you hold as true because you want it to be true.