Lots of people talk past each other on this. Singular they to refer to a known single person is an invention of the last few years and is the thing that a lot of people are up in arms about. It gets confused with the centuries-old usage of using it to refer to an unknown or undetermined person. Your first example is in line with the latter, and your second example is the new usage. TBH I’d be confused by your second example. Is Frank part of some larger group that doesn’t know what they’re talking about? Or is it only Frank that doesn’t know what he’s talking about?