You don't know that they're judging you based on perfect syntax and probably they aren't. Just because someone points out a syntax error doesn't mean they're marking you down for it; maybe they're trying to be helpful.

But that's the problem; there's little or no feedback from most interviews (for legal and other reasons), so many candidates assume the worst.

Yes, the key is to turn it into a technical conversation. Pretend they don't know the answer and genuinely want your help. Interviews are artificial but talking about technical problems in front of whiteboards is a normal work activity. It's not about perfect code but more about coming across as someone they'd want to go to for technical advice on a tough problem.