Anyone can repeat someone on StackOverflow who says that function X really is faster than function Y. That's hardly an accomplishment. It's like asking someone to perform a basic non-trivial calculation out of his head -- why bother?
So they're getting rejected for a reason other than technical skill.
[1] "Okay, we're going to talk like I've already fixed problems A, B, and C, but not X, Y, and Z, because we obviously don't have time for a full interaction that is open-ended enough to allow for all of those to be an issue, and you're being judged on how quickly you focus on and solve the X/Y/Z."
I wasn't saying anything about how one ought to handle such a situation during an interview.
I totally agree that a response akin to "Your question makes wrong assumptions. Let's move on to the next question." would be completely inappropriate for an interview, or if the same issue arose in a normal work situation.
Refusing to do something because it hasn't been profiled is not analysis, it is refusing to do analysis. You have been given a problem and been asked to analyze it. That refusal makes you not a team player.
Once again, this is an interview. Noting that this scenario (a single function that is known to be too slow for reasons that can be fixed in 10 minutes) never happens in the real world is good - it shows you understand that real world analysis includes elements not included here. Stating you won't do this because you don't have profile data is not being a team player.