I had something like this happen to me as well. I was visiting my mother from out of town and set the alarm off when she was at work. I remembered the code too late and the police came. They asked for ID, I have a different last name than my mother. They asked me how I got in, I showed them the key. There was a photo of me and my mother near the door, I showed them. I had obviously been able to turn the alarm off too. They were not nice at all, in fact I would say they were suspicious and curt. In other words, they were doing their job. I was polite and calm the entire time. They left after only a few minutes and I thanked them and apologized for the trouble.
If I wanted to be arrested like Gates, I’m sure I could have easily escalated the situation and managed it.