The problem in this case is that the local hospital(s) did NOT provide that particular technique, but did provide a perfectly acceptable alternative. It was ONLY the person's religious beliefs which created the problem, not the inadequacies of the hospital. Chances are the hospital will eventually include this procedure in their services, at which point that problem disappears. Until then, however, it is only the state's responsibility to provide the AVAILABLE services. If the patient wants something different it's up to HER to find it. And pay for it.
I wonder, though. Would it be possible, in this kind of case, for the state to pay the standard rate for the procedure (in that area) and make the patient responsible only for the difference in cost (including transportation)?