John Doe's apartment

How do you think the scene and for that matter the rest of the film would have played out had John Doe been in his apartment at the time Mills and Somerset came to question him?

We see him as he's walking to his apartment and he opens fire on the detectives. For all he knows they may have more concrete information that he is the one they are after, and that could be why he resorted to shooting, when in reality they have no information other than he took out some books from the library that deal with the 'Seven Deadly Sins' and are there merely to talk and get a feel for what kind of person he is.

Could he have just blagged his way out of the situation and make out he's an innocent? Would he have had to let them in?