If I go to an Italian-language quiz site and see a question asking for "la capitale del Regno Unito", what kind of a derp would I have to be to demand that the answer should be "London", saying that "only foreigners call it Londra"? I'd also presumably take great offence at "Regno Unito", which is off the chart foreign!
Foreigners often have different names for things, it's a pretty integral part of being foreign.
At the same time, it's fun to know the "native" or "matching language" names for things--to know München is Munich, and so forth. And as I've been taking these quizzes, it's really not uncommon that these are themselves trivia questions.
Because users of this site love knowing trivia like this, and love showing it off (to themselves or to others), the urge to want to demonstrate it is strong.
The argument doesn't hold up, but I can understand where it comes from.
The other factor is simply people's desire for quizzes to cater to them so they can excel, and lots of speakers of English as a second language know a cognate for the answer based on something other than the English name--so they feel "robbed" when they get it wrong.