Patek is correct. The pivots can possibly be "dry" after about 5 years or so. This doesn't necessarily mean the oils dried up chemically or evaporated. If the oil creeps away, then the acting surfaces can become insufficiently lubricated also referred to as "dry". Basically, the watch should be service after 5 years of storage not at the 5 year mark. This means if you plan to operate the watch in 10 years or whatever, get it serviced first. If the watch is still not running after the 5 year mark has past, the oils shouldn't cause any damage to sit there but it is unsafe to operate the watch without damage but fine to store. I would store them dial up to reduce any potential creeping to the dial. Does this make any sense? It is sort of like with cars in storage, you don't get the oil changed every 3 months in a car that has been put on blocks and not driven as the fluids, I believe, are usually drained. But if you were going to drive the car, you would need to put the fluids back in before driving the vehicle. I think you are fine. Good luck with your collecting.
TCP