that seems a bit far fetched. I used to live in Mass, and now I live in NH. And i've always lived on the MA/NH border. I've never had any problems. I think as long as your legally registered in your state of residence you shouldn't have a problem. I know in Mass they used to just give out a sticker that you put on the back fender, as well as a registration slip. In NH you get a plate and a reg slip.
I also have never read anything saying that if you were riding in another state you would have problems. As long as you have all the legal requirements in Mass to ride you should be ok in NH as far as I know. Thats like saying your License is so good in another state which is silly. A lot of the people in
Mass DMV's are idiots, they don't know all the laws half the time. Hell, most cops don't even know moped laws.