Possibly might be a restriction. A friend’s daughter was on Medicaid, and her doctor had ordered an epidural block. The hospital said no, because it was not covered by medicaid.
The relatives were all prepared to chip in and pay cash up front.
The hospital still said no. It was forbidden by Medicaid. So you’d have to go to someone and not tell them that you had Medicaid, and no telling what sort of penalty if they catch you.
But that’s just a guess. I don’t know for sure.
Not so for dental, as far as I know.
That's getting increasingly difficult to do unless you use a false identity. Basically have to go out of the country now, and Medicaid clients can have trouble getting visas.