Having been here (legally) for 17+ years, I would concur that there is absolutely nothing that would prevent a Canadian from living/working here, other than their integrity and respect for the law (which, admittedly, Canadian have in abundance) - Well, that and a desire to return home for free medicare, more generous welfare system, ... :-)
The only evidence I have submitted to a half dozen employers of my right to work in the United States (because it's all I've ever been given) - is a cardboard I-94, filled out by me, no less, with a faint, blue stamp and date, and a (once again handwritten, this time by ICE agent) "Class: TN, Until: 07 Oct 2015". No Serial Number, no tracking number - just a stamp and visa class.