A number of people have responded to the key points, but one that hasn't been mentioned is that we have a presumption of innocence. So if a UAV shows up, and you're holding a .45 caliber handgun, we still have to presume you are innocent of the shooting (you may have picked up the gun from the street for example). However, if you take aim at a UAV streaming video back to base and start shooting at it, well that can and will be used against you in a court of law.

There is another issue which is that a hand gun is a poor weapon for shooting down an aerial vehicle. A good marksman, or someone very lucky might do it, but the weapon of choice would be a shotgun. Shot guns on the other hand are not effective at range so in a street fight they aren't a good weapon (great for close quarters, poor for engaging at range).

So in a completely lawless sort of situation I could see teams of shotgun toting folks keeping the UAV population down but not in the typical urban setting in the US.