Kiara is a rational girl said:
I'd like to discuss this. I was wondering, could you describe to me the mechanism by which such a responsibility exists?

It's not a legal responsibility, at least.
Do you have a drug addict/alcoholic in your family? If so, you know the type of heartache that causes for a family. Yes, you can simply say "not my problem" but the truth is it doesn't really work like that.
Sebastian Junger had a terrific interview about coming to terms with what your responsibility is to your friends/family if you engage in high risk activities (he is a filmmaker/journalist that was embedded with US troops in Afghanistan). After his colleague Tim Hetherington died in Libya, he realized the devastation it caused him personally as well as Tim's family and fiancee.
Let me pose this question: if you decide to go sans helmet on a ride to the cafe, and you suffer a brain injury which leaves severely disabled, who will bear the burden of taking care of you for the rest of your life?
You seem to want to drag this out to the extreme and say "well we just shouldn't do anything then!" which is an absolutely absurd stance to even consider. It comes down to a simple matter of preaching and practicing safety first, whether it's behind the wheel of a car, walking down the street, or riding a bicycle. Bad things will happen, but you can and should stack the deck in your favor.
And as far as proving a mechanism, whatever, I've taken enough philosophy at university to understand I can't prove anything to someone with your kind of attitude. But by all means, lawyer me to death. I find it amusing.