See that’s the thing... A close-range blast from a shotgun would cause way more physical damage than a handgun. One would think that a vet and an ex-police officer could immediately tell the difference between a handgun wound, and a shotgun blast. But, perhaps — depending on where he shot himself — the majority of the damage wasn’t visible from the “front”. And, if they didn’t move the body at all I could understand where they could’ve assumed that her bullets were what killed him.
Wouldn't it also, though, take more effort to shoot oneself with a shotgun? So much so that "setting it up" would have necessitated it even being noticed and obvious by people who were not standing that far away from him?