The right to travel by air is an intrinsic right, which can only *legitimately* be removed for the greater good of others, and only with clear evidence that both the greater good of others is in fact real and that the removal of that right is the least intrusive means of protecting that greater good. However, this does not require anyone else to carry them, and does not mean that we cannot, for example, forbid untrained people flying aeroplanes, because that s very likely to be unsafe.
Likewise, you have an inherent right to healthcare: in normal circumstances no-one may prevent others treating you if you desire it (if someone is sentenced to death, you obviously lose that right when the sentence is executed). What is under debate (and I'm not going to get into who is right, that's not important) is whether (a) ensuring that every person can get treatment without finacially crippling themselves and (b) what is the least intrusive way to do this.