It's probably also due to near-gridlock at times which "forces" cars/trucks to force turns when they really shouldn't be--but if they really played by the rules they'd be stuck there. The last time I was in NYC I saw at least a couple of occasions of pedestrians almost being hit (with lots of shouting involved afterwards) for this reason.

It's also true that many NYC pedestrians tend to cut across streets whenever they perceive an opening.