I've seen a lot of Rolexes over the years, particularly when I was in the Navy. This was from 1979-1983 and along with Seiko was the diver I saw most often. Of course we didn't have frogman G-Shocks back then and there wasn't near the number of dive watch manufacturers at that time that you see today. Another reason you saw a fair amount of them was that the Navy exchanges overseas sold them in some locations. I remember seeing an exchange catalog with a date Sub at $600, which was doable for a lot of people interested in buying one. There were restrictions on their sale, however; you had to actually be staioned overseas in order to order one through the catalog at that price.
Plus, the Navy did issue them for some ratings and units. When I was stationed at Bethesda, I walked into the base inventory control department one day and sitting on a desk waiting to be inventoried in a US Divers box was 4 brand new Rolexes with tags and in the green Rolex boxes. Now, why they had shipped them in a US Divers box I can only surmise was to disguise the fact that inside was about $10,000 (civilian market price at the time) of highly desirable watches and possibly because US Divers had a contract with the government to supply them with Rolexes as part of a larger dive gear contract. I don't know for sure, just that there was the 4 Rolexes waiting to be inventoried for assignment to a diving research unit that was a part of the naval hospital base, which contained several ancillary commands.
One other place I tend to see them is at the VA, worn by some of the older vets. As a matter of fact the last time I rode the transportation van to a VA clinic the driver had one on his wrist.