It is up to the medical facility to determine if they will see you or not, or any military facility for that matter. In general most military facilities will not see non-military unless it is a dependent, we had to jump through all types of hoops to get person seen, and that was after a call to the CO of that facility from the CO of our NRD, some facilities are more easy going though.
On the forms there is a spot where you have to put if you were ever denied entry into any of the services, you will need to mark yes and why, the hurdle you have to overcome is that when that medical facility sees that, then that the highest level of waiver turned you down why would they see you, what needs to happen is that you need your OR to talk to BUMED to see what evidence they will need to give you a waiver. It is that specific as I have done it before, I just asked point blank what evidence do you need to give a waiver and in that 1 case is when my guy was sent to a medical facility, in the other cases they said no amount of evidence will lead us to chance our determination.