My objections had nothing to do with the kind of question posed, only the expected response. Unless it's been proven that there can be no way to merge sorted arrays "better" than heap sort, it's flippant and erroneous to expect someone to give that answer. (And there are real reasons to not use heap sort for this.) Even if I don't know that this is the (supposedly) correct answer, they've learned little about my ability to actually merge sorted arrays, and even less about my general ability to solve problems.
Unless they're explicitly hiring me to merge sorted arrays, I'm not going to claim any expertise at at. There are probably hundreds of research papers on this topic, and I haven't read them all, and I know it. I understand that sorting is a big CS topic, but it's not the only CS topic, and I can go the rest of my carrier assuming someone else already solved it and never know how heap sort is implemented and still solve hard problems.
So they shouldn't ask that kind of question and expect such a casually incorrect answer. And they can't tell me "I've already lost the interview" if I don't see things this way, because then that might trigger some manner of hostility. I don't lose interviews when the interviewer expects careless and rote answers. The company loses.