Is it in your job description, that you have to have a car, and that you use it for work-related purposes? And are you compensated accordingly (the standard rate is 56 cents per mile)? I don't mean those as rhetorical questions. It could be that your employer just assumes everyone has a car anyway... I don't know. It's complicated, though. In my own case, my employer knows I don't have a car but am happy to rent one whenever we need one for work. He pays.

At any rate, I don't think you should regard it as your unspoken duty to anyone that you drive a car. It's certainly not something to feel bad about.