Earlier quoted context omitted.
As for the time limit, it's relative. All things equal , if you can complete the problem in 10 minutes and the company can hire somebody that can complete it in 9, then objectively the other candidate is the stronger one. As for nervousness for being forced to partaking in a stand-up performance, I'd argue that "social performance skills" can work against you, since the more "antisocial" you are, the more you can ign…
a single example of a one minute difference in solving a problem that takes ~10 minutes is noise
Or are you going to, as I mentioned in sibling comments, give them a take home task that takes two weeks to complete, just to be sure?