So what is your theory on why Maye did not invite the cops in?
My theory? My understanding is that this occurred when the guy was asleep. He is awakened by someone trying to break the door in. I don't believe that this guy even knew that they were cops- witness the fact that he stops firing and disconnects from the weapon as soon as it becomes obvious that they're cops.
Besides- if he had known that they were cops, what sense would it make to shoot at them if he doesn't have drugs or other contraband in the house? He'd just be setting himself up to be screwed.
First off, there is no reason to believe the cops ever did identified themselves. Second off, it was too damn late to start identifying themselves as they crawled through the window into the child's bedroom.