The thing I always disliked about the food argument is that they do not understand that most all of the immigrant food is Americanized anyway by virtue of making do with what ingredients are available here and if you're making a business out of it you need to suit the palate of the hosts. Most Mexican food popular in America is pretty much just Tex Mex already and it's not arcane knowledge. You don't need the people here to make it. They already don't make it like they would down home anyway. It's always been a disingenuous argument.
Edit: sort of ninja'd. I should also say that the vast majority of ethnic groups we don't see any food get popularized from. Haitian food...uh...Afghan food? no.......most of the Asian foods are brought here by legit immigrants and not illegals.
Can't find it now, but I once saw a documentary about a woman travelling the world, collecting ethnic recipes. When she got to Africa, she wasn't really able to collect any recipes, because they didn't have any. They all ate cassava, taro, plantains, local vegetables, and sometimes a bit of meat. They didn't have special recipes, holiday recipes, or even measurements. They made their food in the same pots and pans and measured that way--two plantains for each family member, then water up to the permanent water stain on the side of the pot.
Most ethnic-American foods are not only Americanized to utilize American ingredients and suit American palates, they're based on the feast-day, special occasion foods of the cultures they're based on. Mexicans rarely eat enchiladas, for example. They eat beans, rice, and a bit of meat, and use torn-up bits of tortilla to pick the food up off their plates, that's the most common Mexican food. They don't even use a lot of cheese, and the cheese they do have is usually white. Also, the vast majority of their food is very bland; all the heat and flavor is in the sauces. Even the salt is in the sauce. If you went by Mexican-American restaurants, you'd think that shrimp cocktails, enchiladas and rellenos, all slathered in melted cheese, are everyday meals. Mexican seafood is particularly egregious, because they serve all the best fish and shellfish in the restaurants, but mostly eat tilapia and trash fish themselves. Fish tacos as we know them, breaded fish, coleslaw, and hot sauce on a corn tortilla, are definitely an invention to please tourists and not a genuine Mexican dish. Their real coleslaw is more like kimchi, pickled cabbage, except BLAND. So bland.
Central and South American food gets more primitive the farther south you go. For instance, I had a Guatemalan chicken "tamale" that still had the bones and skin in it. The corn dough, the masa, was essentially the same, as was the sauce, but the filling was a boiled, tasteless, unboned chicken wing. Totally haram. The Squatemalans mostly lived on one-pot, horrible tasting soups that they would leave out on the stove for DAYS at a time. This is not uncommon for Central and South America, since their power in the smaller villages is not dependable enough for refrigeration in many cases. They eat a lot of deer and small animals they can hunt, as well as eggs and chickens. Guatemalans also eat guinea pigs, it's a national treat. They don't eat them as much when they're in the US, because the pet store doesn't take EBT.