That's not entirely true. My grandmother's family lives in Mexico, however they are are NOT Mexican's, they are Spaniards.
If your grandmother is a Mexican citizen she is a Mexican. She is of Spanish decent.
Art said it better than I was going to try to say. She might have a tizzy, but she is not correct. She's a Mexican citizen, which makes her, basically Mexican. if she doesn't want that, she can look into emigrating back. That said, it's not so easy to move around countries. I've been trying to figure out how to get "back" (considering it was great grands who lived there, back has to be in quotes) to Ireland for over a decade now! Difficult!
On another note, when I was about 19, I asked someone DH & I were sort of friends with (at that time) if she was Chinese or Japanese - I thought she was going to bite my head off. Apparently Japanese don't like to be confused with Chinese. I don't know the reason but boy was she mad.
Interesting. Usually it goes the other way, with Chinese and Koreans having NO interest in being thought Japanese. Something about them occupying their countries and invading and whatnot really cheeses off the Chinese and Koreans!
Interesting offshoot to the discussion...the word that American soldiers liked to use during the Korean War, that word everyone thinks is so rude against Koreans (and it was later erroneously used to refer to Vietnamese people in that war)...means "person" in Korean. Not an insult at all!
Why yes, my husband IS half Korean.
Ok, I just had to Google Sicily and Italy because I could've sworn Sicily was in Italy - thank God I was right

I never knew they didn't like to be called Italian, glad I know. DD is dying to go to Italy and I don't want to get my butt kicked.
It is in it, but they don't admit it. My best friend in HS had a dad directly from Sicily, and a mom whose parents had moved here from Italy. She considered herself to be half Italian and half Sicilian.
OP, you're going to have to speak with this guy from Veracruz about this. Find out why he reacted like that. Perhaps there's some dynamic in Veracruz that made it feel to him like if someone thought I was of British descent, when I'm mainly Irish and a bit Scottish (and a tad Swiss, supposedly, but they just sort of appeared in Switzerland as Hitler was rising in power, so who really knows where that little family was from).
My oldest friend is German, Irish, and Mexican, and she will gladly answer to ANY term for any of those, no matter how offensive someone else might think the words are. She calls herself those things and laughs, b/c words don't mean much to her in that way!
So the fact that this guy reacted like that, you're going to have to ask *him*.