If these people care so much about what us Latin Americans think about word usage, then try to make the term "the US" more commonly used than "American". I can tell you that we most definitely care more about that one than some made-up term for Latino, as there is indeed not a single person here that refers to things from the US as "American", since America to us is a continent first and a country second. "American" is used only of there is no possible way to make "USA" or "the US" sound grammatically natural, which is not often.

But naturally, I am arguing with a brick wall here since I am working under the assumption that these people actually care about our opinion, which they do not. We are just a concept – an ideal to them, not actual people with actual opinions.

The Western version of "Latino" that they came up with without asking the opinion of a single actual Latino on its conception.