While it is true that most private schools accept Canadians, they do not have quotas or limits on the number of international students. On the record, admissions officials will tell you that international applications(yes, Canadians are international down here) are considered in precisely the same manner as American ones.
That said, the difficulty for Canadian students is that in order to sponsor your F-1 student visa, many med schools will ask that you demonstrate the ability to cover ALL four years of medical school. Some schools ask you to send an irrevocable letter of credit or to establish an escrow account with ~$230,000 in order to get your visa. Others schools let you pay by year, and still others will offer you a TA job that pays ~$30,000 per year so you don't have to fork over too much.
Hope that helps. I'll see you all in debt-country.