Actually, with a residential alarm sent, the cops have a need and a duty to verify the ID of anyone they find on the premises. They need to eliminate you as a suspect in a reported residential break-in.
The fact that the cops did not try the doors and windows, even if there were no signs of forced entry, just says they are lazy and incompetent.
That you are surprised at the 20-minute response time is also telling. Residential break-ins are a low priority, unless someone calls 9-1-1 and says they are inside with someone trying to break in. Then you might get a 10-minute response time. Call 9-1-1 and say someone was trying to break in and you shot/shot at them and see just how fast they can get there!