Well of course... but then it is a bit ironic when someone on a BIKE forum recommends taking a car to a bike ride.
I would think it mostly depends on the individual, those who cycle for sport or recreation will have a different outlook from those who cycle for transportation or lifestyle.
I've been car free for almost a decade and cycling has become my primary form of transportation since I got back into riding at the beginning of the year, but I still recognize that its my choices alone that impose limitations as its impossible to accommodate the desires of each individual.
I was out for a morning ride earlier today and witnessed a bad bike accident. It was riding with a group of 5 people heading north on the local MUPl. The guy riding just behind me swerved a little to his right, perhaps to avoid something in his path or perhaps just a momentary lapse of concentration. Went down hard into some trees and bushes. The trail is paved, but if you go off the paved section, even slightly, it is hard to get back on the path safely. It seems like the guy might have hit his head. We managed to extricate the poor guy from the trees and bushes, but called for an ambulance just in case.
Had this fellow not been riding with people, it is possible others riding by might not have noticed him in the bushes, since it isn't really all that visible from the trail. I don't think he was able to pull himself up and back onto the trail and call for help.