If they refuse, the state could recoup the medical costs in several ways
. . .it would seem it only applies to those who do not pay their bills.
It would seem so from that statement, but then the article goes on to decribe one of the "several ways": "It [the state] could withhold some or all of their state income tax refund and deposit it in what Romney called a 'personal healthcare spending account.'"
That's not "recouping the medical costs". Essentially, the article's contradicting itself here.