I presume the Dalai Lama considers himself to be Tibetan.

Now, perhaps you would consider that we ought to demand people's "nationality" be an actual UN member state which counts them as a citizen and since Tibet isn't a member... That's a bit awkward though because the "One China" policy ensures neither the Republic (in Taiwan) nor the PRC will allow the other to be a UN member at the same time as them.

Also I find that I doubt we demand most people have documentary proof. Not taking their word for it is already a bit weird unless you're a border official. Is Samantha Bee really Canadian? I mean, she says she is so I just assumed...