This is helpful background info. While I agree that changing his story makes the individual look culpable, OTOH it should be possible to put together what other facts are known and come up with a most likely scenario. If the parents of the girl feel like it was an accident, that’s gotta be worth something. In many other cases of spousal murder(OJ for one, Brad Cooper for another) the parents feel very differently.
The story I read said that they went shooting together earlier in the day and the shotgun was not ejecting properly. He worked on it when they got home and set it against the wall without properly clearing. Then, later picked the gun up thinking it would be unloaded.