Because, in the absence of other evidence, it's the best take I have.

Also, if the SpaceX president's statement is false, then the fired people probably have a lawsuit to file. Would the SpaceX president be that dumb? Maybe.

It's not about "taking their claims at face value", it's highlighting those claims because that's the one thing that might actually make this firing stick. If the claims are accurate, the employees can't claim that the letter was "protected activity" relating to workplace conditions.