If I entered a building that was supposed to be empty at four in the morning and found someone in that getup, I wouldn't feel safe. On the other hand, I think Missy should have been alarmed just by the fact that doors which normally are closed were standing open up and down the corridors. So I guess its possible that the purpose of staging a burglary was only to fool Missy and cause her to think that this cop was there because of a break-in. Being that I don't believe he was unaware of the cameras, I don't believe the staging was meant to fool investigators. He would have worked much harder on that locked door and moved through the church with more purpose if he wanted to appear to be a burglar. And he would have just worn dark clothing and a ski mask.