NYC went through a major period of "bikelash" when Citi Bike was announced, with people going to batsh$! crazy over the prospect of bike share, and by extension, bikes in general. The system was on the one hand going to be an utter failure and a boondoggle, as no one would use it, and at the same time, there would be blood running in the gutters from all the added crazy cyclists crashing and mowing people down. Needless to say, none of this came to pass. Citi Bike has been wildly successful, despite lots of technical glitches and problems with Alta, the company that ran the system. And like just about every bike share system, it has also had an excellent safety record.
In the midst of the hysteria, there was a rehash of the helmet debate. It was very clear that the people advocating for helmet were the people that didn't want bikes on the street in the first place. I believe a city councilman introduced a bill for a helmet law. He was a well known opponent of just about any street improvements meant to improve safety for pedestrians and cyclists, but there he was crying crocodile tears about bike safety. People who want to mandate helmets are the ones who don't want bikes, and they knew full well that a helmet law would be the surest way to kill bike share, and cycling in general.
Just for the record, I wear a helmet when I ride my own bikes, but not when I ride bike share. If I'm schlepping my bike, also schlepping a helmet isn't such a big deal, but carrying a helmet when I'm just trying to grab a bike and go is more trouble than it's worth. I have to admit that I think I ride more safely on a city bike than on my own bike. Riding a Citi Bike is like riding a Sherman tank in first gear. They're big, heavy, ponderous, and geared really low, so you can only go so fast even when spinning like a madman, so there's less temptation to try to squeeze into small spaces, or dart around traffic. The bikes are also very stable, you sit stock upright, and they have big fat tires, so I'm less worried about getting sent over the handlebars by an errant pothole or something. I fine they encourage a more Zen-like style of riding: sit, spin, go with the flow, and eventually you'll get there.