First, Patek does maintain a list of stolen watches, they just don't share the list with all their Ad's. So are they saying it's OK to bring your stolen watch to one of our Ad's but you had better not send it to HQ?
If you had actually sold the watch, then there would be a paper trail showing some form of sale and the rightful owner would have grounds to have you arrested. You probably also turned this in under a home-owners policy if nothing else, so you have insurance fraud as well. This wouldn't be Patek's probelm, but rather the authorities in that jurisdiction.
When you report such an item as being stolen, quite a bit of information goes into the police report. There are not so many stolen watches of that value floating around, so when the owner brings the watch in for service, he or she would probably have some proof as to how they got the watch if questioned.
If it was simply lost, and reported as stolen, I agree this is more difficult to handle, but watches of this value always have a paper trail. If the new owner states "I found it on the beach." then they would have to show under the jurisdiction they live in, that the watch is now legally belongs to them. Many jurisdictions require a person to make an effort to find the rightful owner, if they followed whatever the local rules were, then they have nothing to worry about.
The reality is that there are two types of owners, those that actually have clear title and those who do not. With a little investigation, I don't think it would be that difficult to discover who really owns the watch.
Take mine for example, I have all the paper work, the reciept, box and so on. Someone else just has a 3940 with no proof to show they obtained it legally.
As I said earlier, it also would sting the grey market a bit.