From a purely physics standpoint, cars/SUVs/trucks ALWAYS have the right of way. I am always shocked when people can't see me in my huge-o work truck, so I never expect people to see me when I am a pedestrian.
However, I'd have to put some rockets on my shoes to be able to go fast enough, to have trouble stopping, like you did ;)
I'm glad that you were able to stop, and yes, that woman was an idiot.
I would have been apologizing profusely if I were her.
I had an 'encounter' with a cyclist when I was driving my truck last year, and although it wasn't my fault, I still felt really bad. I was sitting at a stop light, and the cyclist was leaning on the back passenger side of my truck (instead of putting both feet on the ground). I was turning right (which is legal here on a red light), so when the traffic cleared, I shoulder-checked to make sure I wasn't going to hit anyone in my beast of a vehicle, and started to move forward. I saw the cyclist at the rear on my right side when I looked, and he was clearly stopped, but I didn't notice that he was leaning on me, which was unfortunate, because he fell over on to the curb when I started to drive. Another cyclist that was sitting on my driver's side started yelling at me, as soon as I drove, so I didn't run the guy over or anything, but I felt bad for him. That being said, cyclists leaning on vehicles at stop lights isn't a common practice here. I've talked to a number of my cycling friends about it, and they all agree that it is a dangerous thing to do, and that it wasn't something I should have known to look for.
I try to be even more aware of cyclists since then; Some of them in our city don't pay any attention to traffic lights, and will come zooming out in between cars stopped at lights, and run through the intersection on a red light. It always scares me when someone does that, because it would be much easier to get hit doing that. I've seen a few near-misses with cyclists coming up the curb side past cars that are trying to turn right on red lights as well.