So the place in Singapore that refuses to turn the bezel, they are the actual Audemars Piguet Service Center?? So they received your watch for the initial service, accepted it, and sent it to Switzerland?
I have no idea why they could not turn it 180 degrees. Honestly, I have never thought about this specific situation... of course it can only fit with the brush strokes going 6 to 12, but that leaves 2 choices for how to put it on. I am unsure if it is marked in another manner.
Seems very minor to me, but if you want it rotated, they should oblige you. It is not exactly as if it is wrong - I don't see this as standards dropping - but I understand your point. Still, if AP is going to fix it, why will you lose faith in the brand? Just because you want it done quicker?
If you have concerns over this, I recommend you sell it and move on. I am about to do exactly the same thing with another brand, but in fairness, my experience goes very far beyond yours.