Seems like reuters is lying:
On that basis, it doesn't seem like Reuters is lying. It seems like Reuters has been accused of lying, by someone with a history of misunderstandings with the truth.
It may be the case that they have lied. That would be a pretty egregious act by Reuters. It may also be the case that Elon Musk has reason or incentive to cast doubt on the story whether it is true or not.
Of course the sources could lie but that would make them the liars.
Seems to me Musk is pretty quick to call others liars, but he was also quick to call someone a pedophile.