I'm pretty sure it was just an accident. The father looks like a straight-forward guy on his Facebook page. No signs of anything unusual or anything that indicated issues in the family. I have no indication of what the pistol was, but a Glock has a trigger pull of 5 pounds.
But just out of curiosity, I went in the house and got my G19. I did a trigger job on it a couple years ago and got the pull weight down to about 3 pounds. After unloading it and setting it on the workbench in front of me, I couldn't get the trigger to release the plunger by putting the weight a 2 year-old child's finger would have, on the trigger. It still required that I exert some force to the grip.
So you could be onto something there.