I'll toss this out as speculation, or perhaps just a bit of food for thought.
Many actors who perform in westerns receive training in how to perform a fast draw using a single-action six shooter. Back in the day, most were trained by Arvo Ojala. (Side note - Ojala did a little acting himself, and he was the "bad guy" that gets gunned down by Matt Dillon in the opening of Gunsmoke.)
The technique that he usually taught involved "cocking in the holster." As the draw began, the shooter thumbed back the hammer before the gun cleared the holster and held the hammer back. As the gun cleared leather, the shooter pulled the trigger back, so the only thing preventing firing was the thumb on the hammer. The draw continued, and as soon as the gun was level and pointing at the target the shooter would slip his thumb off the hammer, firing the gun.
This method is blindingly fast, and Ojala was timed at drawing and hitting his target in less than 1/6 of a second.
It's not too far fetched to think that AB learned this method during his career. To be smooth and fast, it has to be practiced until it's done automatically, without thinking.
It's possible that AB drew the gun in this manner and it fired when he released the hammer. He might be unaware that he was already holding the trigger back when he cocked the gun and took his thumb off the hammer.
Just a theory that might satisfy the incongruity of his tale. And if the theory is correct, he's certainly responsible for firing the gun.