As you point out, there are externalities here of sorts. Government healthcare is often considered bad by libertarians as it seemingly gives the government the right to control people's lives (e.g. oblige they do exercise or not eat red meat or not have unprotected anal sex or whatever) in the name of reducing the costs on the healthcare system.

That said, if an opt-out was allowed to be used by the mountain climber or couch potato or go karter or bare backer that states the government has no obligation to help in the event of a bad outcome caused by their activities then the "externalility" disappears.

This is noteably NOT the case with the more classic examples of externalities such as pollution. Doesn't matter how many waivers the polluter signs, other people still get lung cancer.