SPHLC
I went private some years ago for an op on a broken foot (which the air force had ignored for a month) It cost me about £1200 (a lot then!) and, after putting myself off sick post op for a couple of weeks, I duly pitched up at the sqn ready to fly.
The Boss sent me straight to see the MO, who then decided to ground me, explaining that aircrew can't do this sort of thing etc.
After presenting the MO with the bill for the said £1200, and pointing out that I would let the nice civilian surgeon know what the MO had said blar, I was suddenly allowed back to fly! After further (heated) discussions about the £1200, bad publicity etc, I got the said amount refunded.
I hate to say it, but it depends very much on how big your ball$ are, and how much you value your career in flying.
The medics won't understand anything other than medic stuff, so it's no good trying to 'negotiate' with them. As you have found, they will only cover THEIR arse$ (certainly not yours)
Take them on, stand firm against them, and if it all gets nasty, explain that the 'missus' might have to drop a line to ???
Good luck
The Swinging Monkey
'Cauthers, is it time for my afternoon tipple yet?'