Some states require titles and some do not. Ohio doesn't, but Pennsylvania does. I can go 30 miles from home across the state line and buy a moped with or without a title, maybe not even get a bill of sale, and I haven't had any problem (yet) getting a license plate.
I went to the Pittsburg rally in mid September and a PA guy was riding a moped bought and plated in Ohio, as his parents live in the Akron area. Some states are more strict than others.
What issues do you have in Quebec, and are they the same issues all across Canada? I'm sure newbies (and myself) would be interested in the laws in Canada.