That's a fair point - I didn't know you could opt out.
However, IMHO in the aviation context there is little to gain in opting out since the CAA or FAA can demand your GP record anyway, and if you go to another GP he might well contact the one where he knows you live "out of courtesy". He will certainly ask you for your normal GP's name and address. When I was about 30 I was taken to casualty after a windsurfing accident and when they wanted to know the name of my GP and I said I have never seen one they looked at me like I came from Mars.
Sure most pilots are scared of seeing a doctor until they have clear symptoms of something really serious, but the only sure way to get seen discreetly on something you merely suspect would be to go abroad, I suspect (never having tried it).