Does this extend to all behavior that can be shown to be statistically more likely to result in injury, illness, or death?
Ahh, the slippery slope argument. The answer is of course we don't extend it to everything.
So, we apply it to things like vaccinations, but not throwing rocks. Excellent. Except I imagine more kids die each year from reckless behaviour than are killed by chicken pox (the ad promoting the chicken pox vaccine listed between 200 and 300 kids a year dying in the U.S. from chicken pox). That's right, it's less than 1% as risky as the flu, and people blow that vaccination off on a yearly basis. I'm not sure what your risk of negative outcomes is for the chicken pox vaccination, but it can only be slightly lower than the risk of not getting it before the risk is nil. So do we still shut out the kids who didn't get the chicken pox vaccination?
As usual, broad, sweeping statements are usually wrong. Do try to learn something from the bad behaviour of politicians.