Jim, I looked at the Alyea film again... The narrator does say "there's an officer with the gun"... The officer is looking out the window and then walks toward the camera. The gun he is holding really looks like a pump shot-gun, in my opinion (if I'm actually looking at the same one you mention). It would be good if we had better film copy to analyze...
But yes, I agree. On site where the gun was found, there should have been positive identification without any question or doubt. Instead we get "it looks like... he said it was..., etc."
We're either dealing with the Keystone cops, or there is something else, perhaps sinister, going on with the Mauser issue....
Jake