That is one of the questionable questions. According to the big fat Oxford English dictionary "gotten" is a N. American *slang* word. Yes, it is in common usage in the States, but in Britain they look at you like you have two heads if you use it. So I think that it is incorrect of her to say that "gotten" is a right answer. It may be common in speech, but technically it shouldn't be correct in a test of this nature.

And I chose "got/their" both times that I took the test last night and got 100% for that section on my second try (using all the same answers both times), so maybe she has both choices set up as correct.