@sferik—I’m intrigued as to why you think that non-Spanish-speaking Americans would sound like ignorant gringos if they would pronounce Mexico the Spanish way as opposed to the US American/English-speaker’s way.
I feel like Spanish language is so prevalent in the US right now (or, at least it is in LA where I live) that it is not uncommon for non-native speakers to know SOME Spanish, even if it’s just the correct pronunciation of Mexico and other Spanish words. I will admit that it does sometimes seem a little out of place when someone is speaking English and then goes to pronounce some parts of the sentence with a Spanish accent like, “The mayor of Los Angeles, Antonio Villaraigosa, held a press conference today in the city of La Puente” and they pronounce the Spanish parts as they are meant to be pronounced in the Spanish language. It seems a little out of place perhaps, but I don’t think that it makes them sound ignorant at all. Why would they? They’re just pronouncing a Spanish name with a Spanish accent.
PLUS, I just thought of this: if you hear a white person say a sentence with Spanish words and she pronounces them with a Spanish accent (example: “My friends and I are planning a trip to waa-haa-kah, meh-hee-coh (Oaxaca, Mexico)”), how would you know whether they are Spanish-speakers or not? How could you determine based on that sentence if they are ignorant gringos who only know how to pronounce Spanish words with a Spanish accent, or people who have actually studied the language at length and just pronounce the words as they are meant to be pronounced? To me, I don’t think that either person is ignorant.
I ask because I’m a Caucasian Spanish speaker and I wouldn’t want people to label me as an ignorant gringo if they heard me using Spanish words the way they were meant to be pronounced in an English sentence.