I think that last paragraph is just referring to actually using the hair itself. As in, you can't exactly collect a thestral hair if you can't see it. As far as using the wand, I don't think that would affect it. Still though, to use a core that we only know to have been used in what is the most powerful wand anyone knows about is kind of much. 

I mean according to official information, Ollivander only trusts the main three we know about to be of good quality. Yes we could have something else, but unless there's some justification I imagine any wand not using those three cores would cause some trouble with its owner.