Pronouncing Foreign Places

A pet peeve I've always had, is when people get obsessed w/ pronouncing foreign places in the native accent, while everything else in their sentence stays American.

Example:
(pronounced their normal way) "Oh, yah, and in my Junior year of college I got to go to
( hispanicized with a clicked r) PAY ROO
(back to normal) for the year"

Not only is this kind of jarring, but silly, in my opinion. First of all, if you had said you had gone on a trip to England, would you have used a British accent when you said England? It also always feels to me like the people might be overeacting to American egocentricism. Like they're thinking, "Oh, it's so American to think it's actually pronounced that way. They should really know how it's really said."

Now, I realize, that's how the other countries say it, but there's nothing wrong with languages altering a place name to fit their language. For instance, would you correct a Spanish speaker for saying Estados Unidos?

All this being said, I do think the country Chile causes some problems. I maintain, that saying CHEE LAY sounds pretentious. But calling it chilly does sound a little dumb. I think the answer lies somewhere in splitting the difference, but am curious on where others stand on this highly controversial issue.