Yelling "POLICE"

I've been reading about this "Cory Maye" case, where a guy shot some cop who bust into his house. There is controversy about whether or not the police announced themselves before busting in.

My question: What's to keep an armed robber, rapist, or murderer, from shouting "police" to gain entry to someone's house? I mean, if they said "Open up, it's the police!" people might be more willing to open the door, whereupon the bad guy can simply shoot them in the face and leave.

So what's the big deal about yelling "Police"? It seems meaningless, if you have no proof the people at your door really ARE police.