Very interesting document.
I heard the same about Prieur and some other ADs all over France.
It is clear that Rolex didn't deliver these 5513 directly to the M.N, but that the M.N bought them to ADs.
The thing is that PRIEUR won't help us to have more informations;, sadly.
In the case of mine, it was sent to Geneva for a service, BUT the most important is its provenance.
The seller was one of these few guys who was in relation with some militaries from the French Marine.
And it was part of a lot....
Best,
Nicolas