Victims of crime is already an accepted practice in healthcare. Most (if not all) medical facilities have financial counselors that help victims qualify for such aid and can pay up to 100% of the costs. In addition, the financial counselors will also try to enroll patients in medicare/medicaid/obamacare/other government aid depending on if they meet federal poverty guidelines or criteria. This is standard for all uninsured patients as well. I'm not certain if all states have victims of crime aid and if they do have aid how that relates to the federal government, but this is already well established.
Also, just because healthcare is relatively private (which isn't a fair statement) doesn't mean facilities don't take advantage of such programs. Hospitals want to and actively do enroll patients in welfare. Welfare will pay the bill, patients don't.