Of course they can. I've been calling for that for ages now.
The problem with that petition is that it treats Axanar Productions like a legitimate studio that's just been mismanaged by Alec Peters, and if only someone else in the organization would topple him the roadblocks to the Axanar film would be completely swept away. It ignores two basic facts:
1) Peters and Axanar Productions are a package deal. (They even have the same initials.)
2) You don't actually need either of them to film the battle of Axanar.
You see, if there's anything Peters has done successfully it's that he's so closely associated himself with the story of Axanar that too many people think you can't have Axanar without Peters or his companies. I think proving that idea wrong will go a long way to finally breaking the hold on his cult.
The cult would want peters to sue for copyright infringement. Him and then tihiks he owns the axanar universe.