In the NYC subway, I think it would have been acceptable for that assistant to just walk up and say, "Excuse me. We're trying to shoot a movie, here. Would you mind backing off, please."
Minding every "P and Q", and trying to be perfectly polite isn't always necessary, especially in a place like the NYC subway. In some cases, being TOO polite could set a person against you just as much as if you were totally rude. The perception of politeness varies with the location and situation.
Construction workers on a job site would probably be justified in shouting, "Hey! Out of the way!" but the same thing said in the public library would probably get you tossed out.
If that woman would have approached you at the gazebo in the park and said that she was a photographer and that her clients wanted to have their wedding pictures taken at that location, I'd expect your reaction would have been completely different.
It doesn't matter whether the photographer is using the most complex, 8x10 large format camera or a digi-snapper. More than half of the photographer's job has nothing to do with the camera, the film, the computer or any other kind of equipment. It has everything to do with how you relate to people. A gruff photographer is probably not going to get a flattering wedding portrait out of a newlywed couple, especially when he runs around ordering people out of his way. It takes somebody who knows how to talk to people and make them feel good about doing what they are asked.
It's not what you say but how you say it.