I mean, I'm not offended, because this never happens to me, because I'm white. But I'm given to understand that national pride is as important to Central and South Americans as it is to anyone, and this is something that matters to many expats, and it's not hard for me to understand why.
Try calling your average middle American a Russian (same difference, right?) and you might be in the ballpark.
Mistaking a Chilean for a Mexican is no more offensive than mistaking a German for a Swiss (or a Spaniard for a Portuguese). If you think it is, then I strongly suspect you are actively looking for opportunities to be offended, for your own reasons.