The co-pilot in this case could very well be the armorer, and I have read some reports that he/she was apparently firing live ammunition during breaks.
If that's true, that's monumentally stupid.
But a weapon firing is physics. If a revolver is not cocked, you can't make the hammer fall until you cock it.
You can do that by pulling the trigger. That takes a lot of pressure. Or you can pull the hammer back to the ready position and then the trigger pull becomes easy.
Or...as I posted...you can fan the weapon which means you bash the hammer back to the full back position, which takes it past the catch so that it will then fall and hit the primer of the round. But that still happens by someone's action, not by accident.
The negligence in this situation would be for there to be some type of live munition in the chamber when it was unexpected.
A revolver going off accidentally, unless it is in a cocked position, would be like finding a unicorn.
Revolvers are different from semi-automatics. It would take some serious physics if the hammer is not back to discharge a round, whether blank or live.
Alec Baldwin very likely provided the physics. It may not have been his fault, but you don't shoot somebody with a revolver just by pulling it out of a holster unless it is already cocked. Knowing whether it is cocked or not, is a pilot responsibility. And yes, knowing what is in the chamber ultimately falls to the person providing the physics. (Unless contracts specifically hold that person harmless)
Colloquially, they might call it an accident. But legally, there was probably negligence. And unless there are very specific hold harmless provisions, Baldwin may have some culpability. He was the pilot. He provided the physics. It's almost impossible that the gun fired itself.