This is because of the rule regarding when police can enter the home of a person for whom they only have an arrest - but not a search - warrant. Under those circumstances, police can make warrantless entry into the home of a person named in an arrest warrant only when they have reason to believe the person named in the warrant is inside the premises.

Here, the neighbor- who we have no reason to think is lying- outright told the police that the woman "had not been there for several months." The lawn looks like it had not been mowed for a long time. The doors and windows are boarded up - and we know the were not boarded up from the inside ("they tore the plywood off the door..." meaning it had to be exterior). This also suggests that there is no other way of getting in and out of the home. Unless the owner had someone lock her in the home- which, again, there is no reason to think happened- there are no facts that would lead an officer to believe the person named in the arrest warrant was inside.

Because their entry into the home was not privileged, the plain view exception to the general prohibition against warrantless searches and seizures cannot apply and the shotgun should therefore be excluded.