While I don't think correcting an interviewee is inappropriate, it's probably not the norm. I've never experienced it as an interviewee nor have I done it as an interviewer, and I (personally) wouldn't. Then again, it's not my personal style to ask questions in face-to-face interviews that have right or wrong answers (note: I ask questions for which there are good and bad answers, but not really right or wrong -- YMMV).
When I interview someone, I'm also (as others have alluded to) watching for the way the candidate works out the question or the problem asked. By asking open-ended questions, I then have the freedom to ask follow-up questions that can probe deeper into thought processes and also behavior. By "behavior" I mean does the candidate always have a ready answer even if it's not the "best" answer or is illogically formed? Or do they pause, consider their answer, and give a well-reasoned one even if it takes longer? Or, vice-versa, of course -- all outcomes, right or wrong, provide insight. My goal is not to shut down the conversation, which is how a verbal correction might be interpreted.
Now, depending on your circumstances and the types of jobs you're interviewing for -- such as whether or not the candidates are right out of school or otherwise entry- or junior-level folks -- I can totally see having a mix of questions. And, I can even see the benefit of correcting someone who says something wholly incorrect -- but it would be for the explicit purpose of seeing how they respond to criticism, not just to inform them that they're wrong (although that's a good side benefit). As you saw in your snarky candidate, someone who doesn't take criticism well in an interview is likely to take it less well in an actual working environment, so it was useful.
TL;DR: I've not experienced it, it's not inappropriate and is potentially useful, but perhaps spend some time determining just what it is you really want to know about the candidate and tweak your process accordingly.