So in this case, the way to ensure no one knows you're from the US military is to wear a completely unique watch, with no external markings, but a nice BENRUS on the movement....
I always thought the point of unmarked equipment was not to provide deniability for the person themselves, after all, they can be treated as spies, but to erase links to the government that sent them.
I don't buy the covert operator story behind this watch....Just illogical.