Actually I think rolex movements quite popular so those more experienced watch makers should have no issue servicing. Only problem is if any part need to be replaced - where are they going to get genuine parts from? Scavenging is a popular practice (even in car workshops) to get the watch out asap. Some even got pre-serviced movements (subcontracted to home-based watchmakers to service) so they do a direct swap and pass you the next day - you still get a genuine movement but it isn't your initial one, yours will be serviced own time own target by a subcontractor and returned back to the watchmaker for the next swap.
My father's friend is a watchmaker, and I witnessed him subcontracting movements (I learnt from my dad that he does it to popular rolex and omega models) to his trusted friends to service. Needless to say I never gave him any business, but such practices are prevalent nonetheless, especially when you bring the watch to service and ask for it to be done within a few days to wear for CNY.
I only serviced rolex twice, and both times I requested for the movement number to be recorded on the invoice, when going back to collect, I ask the watchmaker to show me the movement number again. Of coz, I need to have some comfort level that he doesn't swap other parts lar, haha.