How many military watches end up in civilian hands? No shortages of those being sold currently on this forum. NASA shouldn't be different than Army/Navy...
Also would think there has to be something regarding the time frame as well...anyone who has spent time in the military or government has "acquired" things...perhaps "acquiring" a sleeping bag is not the same as "acquiring" a watch, but at some point, that sleeping bag will end up in a military surplus store so what is "wrongful possession" at one time is not necessarily "wrongful possession" 20-30-40 yrs later...
Particularly if the item in question has been "decommissioned".
Either way, you could take unofficial routes to ascertain the validity of the watch.