"Because if the cops found it inside the house they have you dead to rights. If it's in a backyard you can claim someone else ditched it there."
That makes zero sense. First, it isn't illegal to own or keep a shotgun in your home in NO. Second, there is no direct way to tie a shotgun to a shooting (no ballistics test). Third, your fingerprints are going to be all over the gun anyway in most cases. The only reason to store a gun outside a house is if you need fast access to it when you're in that location.
If you're not legally allowed to own a firearm because you're on parole or the weapon has been illegally modified is a good reason to not keep it in the house.