Musk is a minority shareholder in SpaceX which owns Starlink. One corporation (SpaceX) is not supposed to be liable for the actions of another (X), even if they are owned by the same person.
Musk doesn't refrain from using his companies, mainly Twitter, as weapons in petty personal disputes and showdowns. It's a situation that allows piercing the corporate veil, even under US law. See https://en.m.wikipedia.org/wiki/Piercing_the_corporate_veil#...
The correct move is to go after Musk directly.