I'm not sure if anything similar applies to rolex, but I can tell you my experience with my grandfather's patek. Since it was a pre-1975 model patek does not "service" anymore (read: through an accredited more or less local watchmaker), but "restoration". That's also because the parts may not be available anymore and in that case will be actually manufactured anew. That means that the watch had to go to Switzerland. Well, to Munich first, for the assessment and then to Switzerland. After the assessment, if you refuse the quotation, they will send it back to you, but via insured value mailing service which you would have to pay (around 400€). I went the whole nine yards and they actually changed the hands, which had a nice patina, alas, but there was some humidity inside. Enamel dial remained thank God.
Now to your case, I don't know what rolex policies are, and probably rolexes are simply more widespread and it's easier to source spares. In your case I would simply go to a watchmaker that knows his craft. A patek would be another matter, I don't think many actual watchmakers have ever seen the movement inside my grandfather's patek.
Not to mention the cost...