Now I'll back up a bit and turn it around. Yes, the narrowest of solo canoes should have stability. Not the dreary, raft-like stability of the flat bottomed standard canoe, but the lively, dynamic stability of a living thing. Firm final stability, however, is absolutely essential in a touring boat. This is the feature that permits the canoe to roll through its arc, begin firming up, and then STOP before the rail goes under.
Final stability is the result of hull design, and has nothing to do with width.
Many racing canoes utilize excessive tumblehome for paddling convenience, sacrificing reserve and final stability. I have found this type of canoe to be rather vicious and unwholesome and entirely unsuited for touring. A good test is to kneel in the canoe, grasp the gunnels and roll it from rail to rail. If you dump, you might keep shopping. Stick with editorials and articles in Wilderness Camping for your information.