Personally, I've always felt that it made more sense to wear my watch on my primary hand, with the face on the back of the wrist. This was a decision I made as a kid, back when writing was something I did with a pen. The idea was that if I was going to be sitting looking at that hand anyway, it would be a lot easier just to tilt it a bit than it would be to shift my focus to my other hand. My oldest sister is one of the few people I know who agrees with me.
One of the other people I've heard of who wears his watch on his primary hand may be the cause of Lab's vague recollection. He's a friend of a friend who is somewhat paranoid. His thought was that if he wore his watch on his right hand, a potential mugger would have the opportunity to notice that and thereby assume that the victim is a lefty. This would give him a slight advantage if things then came to a struggle. It doesn't make much sense to me. I don't know how many muggers are really that observent. I don't know how many would get that close to their targets without being very aware of any movement. I don't know how many of the observent ones would be observent enough to notice other things, which might give away the ruse. But hey, if it makes the guy feel better, good for him. <shrug>
Paul