It's also not really a choice NOT to participate in modern, American healthcare.
One of the proposed "fixes" originally was only to "require" insurance of people that partake of the healthcare system which is, at some level, everyone born in the United States. In other words, if you've never or will never use any healthcare, you'd be freed of the obligation. There are lots of practical problems with this, including, what to do with "free riders" or protestors that show up to a hospital, clinic, etc. when they're already sick or in need of healthcare.
And when people tried to posit scenarios of someone who would never need U.S. healthcare, you get politicians like Rep. Steve King citing babies discarded in dumpsters. http://www.youtube.com/watch?v=OOrBpTdZ2tc&feature=player_embedded
The fact is, everyone participates in the current healthcare system even if they don't want to. Even those that affirmatively try to avoid the system could wind up there nevertheless via an ambulance and a 911 call. Allowing certain people to NOT participate is highly inequitable and without any rationale basis.
All of that said, this result of the ACA is largely the Republicans' and insurance companies' fault. The more sweeping, Democratic vision would not have had the same problems and would not be unconstitutional on these grounds.