I've been in this situation several times so far.
Once it was a practical problem given for me to solve (maths was involved - only one solution was correct). The interviewer corrected my solution, but I was sure the solution was actually ok. So the question was: should I try to convince him knowing he will probably hate me for pointing out his error or just accept his error hoping it won't influence my chances to get the job too much. I went for the first option but I was very diplomatic, I proposed we analyse it together, asked questions to make him understand his mistake, which was really evident, etc. We ended up having a long discussion on that and him telling me I had no idea. A few seconds later he actually told me I was right - and looking at how furious he was (he was so nervous he actually spilt some of his coffee on me) I knew I would never get the job.
I didn't get the job. The feedback was I didn't come across as assertive enough.
Now another situation like this. I was given a brainteaser which required me to guesstimate one economic indicator for my country. When explaining the solution to the interviewer he told me I was completely wrong and the indicator had actually a much lower value. I didn't want to argue this time as I wasn't completely sure. Now I checked it. I was actually very right, I missed the correct indicator from last year by less than 5%.
What is the right way to deal with the situation when the interviewer is wrong? The goal is not being eliminated as a candidate.
I don't think the linked question is the same. The question from 6 years ago seems to suggest that the interviewer was trying to test the interviewee's reactions (by repeating the same question many times in a very confrontational way, etc.). It seems to have been a typical stress interview. I've had that before, but the situation I describe in this thread is different. In this case I'm convinced the interviewers were actually mistaken.
Moreover, my question is not, "how to tell a interviewer that he is wrong", my question is how to react to this kind of situation - whether it makes sense to tell them or what better alternatives there are.