That is exactly what I am saying. If he has a solid address, it is unlikely that he is a small time burglar.
Not sure how IDs work in the US. In Germany you have to register with the police when you move and you are supposed to carry your ID at all times. Of course there is no guarantee that people keep their ID up to date. Then again, I suppose if mail to the old address would be failing it could be marked in the computer, easy to check for the police.
I think you need to multiply P(is a criminal) with <severity of the crime>. If they suspect somebody of being a serial killer, more scrutiny seems appropriate than if they suspect a small time burglar.
I don't see "Serial Killer" levels of scrutiny in this story. I see the right amount of scrutiny, but with a precursor of a cop getting his gun hand ready in a situation that doesn't call for it.
Back to this story: you have to check out whomever matches the description and is nearby. The only thing that the police needed to do in this situation was to not make it a situation. Reaching for that gun was The Wrong Thing To Do because this guy was cooperating.