I have a .22 that my Dad modified for a really light trigger pull - between the gas ramp up front and the light trigger, it is great for competition shooting but if the safety is off and you give it a little jar, it is possible for it to fire from it.
A gun in disrepair may have issues too - being hidden in a sock raises questions about how long and what condition.
If he knew it was a gun, why would he shake it out of the sock into his hand, and not take it out carefully?
If he didn’t know what was in the sock, why would he shake it out of the sock into his hand, and not onto a table or floor?
Not that there couldn’t have been an accidental discharge either way, but I just don’t buy his story. He shakes the sock (either knowing it was a gun, or not knowing what it was), into his hand, it lands perfectly aimed at his coworker, goes off, and hits her in a vital area causing her death. While technically possible, I have serious doubts that it actually happened this way.