We aren't mexicans! The fact that we were born and raised in Mexico is pure semantics.
Ummm:
1) You obviously have spanish heritage
2) You were born and raised in Mexico
Yep, that about fits the definition of "Mexican" to me. 
If... they've naturalized wherever they are now, and it's not Mexico, then. Yeah, they're no longer mexican? If someone spent the first, say, five years in one country, and then then next 10-20 in the one they're in now... I'd say they're of the latter, m'self. They're
from Mexico, sure, as per Tomato, but I wouldn't particularly consider 'em
mexican anymore.
I can see where they're coming from, and I do imagine it's a source of great frustration for a lot of immigrants. Y'spend decades of your life in another country and they still label you as "other", despite you being one of them in basically every way but
maybe skin tone and a few years back when you were a kid. Annoying, at the very least.