I should have put a smiley face on my last post here, but my point is that turning the tables on someone can sometimes be your most effective course of action.
I also think it helps a lot to carry yourself with an air of confidence and self-assurance, and to be firm without being confrontational.
I've been stopped once for photographing, in the richest enclave in Ft. Worth, TX while accompanying a friend who was doing a photo essay on rich and poor. He was shooting houses (the Tandys of Radio Shack and neighbors) and I had a telephoto on, taking pictures of downtown from a distance. We were shooting from a public street.
The police who tried to chase us off threatened to confiscate film, etc. They backed down after we firmly asserted our rights and demonstrated that we knew what they were. It helped to mention the names of some friends, including a newspaper editor, a well-known police detective, and a friend who was clerking for the county courts. We also dropped the phrase "illegal search and seizure". That was nearly 30 years ago now, but it was the last time I was confronted for photographing. But to be honest, my first instinct would still be to start photographing someone who was watching and tailing me.
If we don't assert and defend our rights as Tanya did, they'll erode away.
Oh, and it wasn't you who pulled the police from more important things, it was some paranoid who watches too much TV, doesn't understand what to take seriously, and insisted to the police that you were a dangerous photographer.