In fairness, "fusion" or "pan-Asian" isn't pretending to be something specific... it's borrowing from other things to create it's own genre.

That said, in general I have some sympathy for complaints about authenticity when it comes to "truth in advertising" - as an expatriate NYer, while I like quite a variety of styles of pizza, it always bugs me to see people claim that pizzas are "NY style" or "NY pizza" when they're about as much NY style as Pizza Hut's pan pizza is "Chicago Style."

As for Mexican, while local places are often much better than chains, what you're likely to find around here in California Mexican which is pretty much a distinct style in itself rather than being an authentic match for any particular regional Mexican cuisine.