Medicare, fund comes from Federal. Medicaid, fund comes from State. Both are short and shorted right now. My parents didn't have 40 points. So they were not eligible for neither Medicare nor Medicaid as GC holder.
What I did was: pay them every year and hopefully they'll have enough points one day; wait for 5 years to see whether they want to apply for citizenship; and apply for charity program from hospitals directly.
So that charity program is for "big deal". I'll take care of everything else at this moment.