For sake of testing your position, let's assume the fraud is true and he does what you want and publishes the details like that.

What about the corner-case person who actually is legitimate and now has incredibly private information out there to make stealing their identity trivial? As a statistical anomaly who is often that corner case, I'm glad you're not the one making the policy. I wish Elon wasn't as well, and I'm sure there's going to be a giant mess at the end, but using government power (which Elon has, whether rightly or wrongly) to publish personal information about people (which they get by force giving their monopoly on government power) especially without trial or due diligence is very wrong IMHO.

This is what courts and process and testimony are for. Doing this reliably in the face of bad actors with minimal stepping-on-fingers is a solved problem.

Unless you don't actually care about the truth and want to send a convenient lie twice around the world before the truth gets its pants on. Then you should act like Elon is acting.