Honestly, I thought Tyrion's scene showed how parochial he was, not her (and was meant to do it). There were a lot of parallels with it and the scene between the high sparrow and Olenna Tyrell in the high sept the week before. Olenna and Tyrion are masters of the Game of Thrones, but their stuck in a world where the great houses are the centers of power. Now that Ice and Fire are coming, it's not clear to me that their cleverness is really going to do them any good moving forward, at least if they can't shift their point of view.
Ah but I disagree, because the reason Tyrion has survived as long as he has, despite everyone's best efforts to destroy him (both literally and politically), is because he is NOT parochial like everyone else from the major houses. He recognized early on that his name wasn't enough, and so made his way through being Hand of the King by having a wide understanding of everything around him.
He knows how and when to use his name to effect, but also when to circumvent his own name. He knows how to relate to the major players, as well as the little people. He knows how to deal with enemies on the outside while holding off enemies from within. We have seen all of these things, and so we see just how widely Tyrion is able to view everything.
Of course, he does have a track record of stubbornness and ignoring his own best judgement when it comes to personal matters, but in terms of dealing-with/defeating/protecting/counseling the masses as an unsung hero, he knows what he's doing, which is why being with Danaerys makes him much more dangerous.
I'll have to watch the scene again, though. Perhaps the show is trying to make him vulnerable in order to exaggerate how much he needs Danaerys, just as we know how much she needs him. Because regardless of his wide/narrow view on things, it is true that they need each other.
