That may be changing (in any case, I personally would support having it as a backup):
http://www.cbc.ca/canada/story/2005/06/09/newscoc-health050609.html
Top court strikes down Quebec private health-care ban
Last Updated: Thursday, June 9, 2005 | 9:33 PM ET
CBC News
The Supreme Court of Canada ruled Thursday that the Quebec government cannot prevent people from paying for private insurance for health-care procedures covered under medicare.
In a 4-3 decision, the panel of seven justices said banning private insurance for a list of services ranging from MRI tests to cataract surgery was unconstitutional under the Quebec Charter of Rights, given that the public system has failed to guarantee patients access to those services in a timely way.
As a result of delays in receiving tests and surgeries, patients have suffered and even died in some cases, justices Beverley McLachlin, Jack Major, Michel Bastarache and Marie Deschamps found for the majority.
The Quebec government reacted by saying it would apply immediately for a stay of between six months and two years before the decision takes effect, given the chaos it could cause in the delivery of medical services in Quebec.
*****
I looked online and it appears that you can purchase private health insurance in Canada:
http://www.canadian-family-medical-plans.com/
Health & Dental Insurance for Canadians
Are you looking for a medical dental plan similar to those offered to people employed through a company?
We have teamed up with Manulife Financial to offer the same plan that many companies and large associations offer but with no membership or company affiliation. Take advantage of the stability and efficiencies of being part of a group with over 1 million members in Canada.
The Canadian Family Medical Plan offers these advantages at no additional cost. Get a quote now.
http://www.eridlc.com/hr-laws/index.cfm?fuseaction=hrlaws.private&country=canada
Private Health Insurance Plans
In Canada, the term, private health services plan, ordinarily applies to some or all of the following:
extended medical insurance, such as prescription drugs and semi-private hospital rooms
dental benefits
vision or eye care benefits
http://www.canadian-healthcare.org/page4.html
Private Health Insurance
While the health care system in Canada covers basic services, including primary care physicians and hospitals, there are many services that are not covered. These include things like dental services, optometrists, and prescription medications.
Private health insurance plans are usually offered as part of employee benefit packages in many companies. Incentives usually include vision and dental care. Alternatively, Canadians can purchase insurance packages from private insurance providers.
The main reason many choose to purchase private insurance is to supplement primary health coverage. For those requiring services that may not be covered under provincial health insurance such as corrective lenses, medications, or home care, a private insurance plan offsets such medical expenses.
While private insurance can benefit those with certain needs, many Canadians choose to rely exclusively on the public health system.
http://www.capmag.com/article.asp?ID=4271
Why Canadians Purchase Private Health Insurance
by Walter Williams (June 20, 2005)
America's socialists advocate that we adopt a universal healthcare system like our northern neighbor Canada. Before we buy into complete socialization of our healthcare system, we might check out the Canadian Supreme Court's June 9th ruling in Chaoulli v. Quebec (Attorney General). It turns out that in order to prop up government-delivered medical care, Quebec and other Canadian provinces have outlawed private health insurance. By a 4 to 3 decision, Canada's high court struck down Quebec's law that prohibits private medical insurance. With all of the leftist hype extolling the "virtues" of Canada's universal healthcare system, you might wonder why any sane Canadian would want to purchase private insurance.
Plaintiffs Jacques Chaoulli, a physician, and his patient, George Zeliotis, launched their legal challenge to the government's monopolized healthcare system after having had to wait a year for hip-replacement surgery. In finding for the plaintiffs, Canada's high court said, "The evidence in this case shows that delays in the public healthcare system are widespread, and that, in some serious cases, patients die as a result of waiting lists for public healthcare. The evidence also demonstrates that the prohibition against private health insurance and its consequence of denying people vital healthcare result in physical and psychological suffering that meets a threshold test of seriousness." Writing for the majority, Justice Marie Deschamps said, "Many patients on non-urgent waiting lists are in pain and cannot fully enjoy any real quality of life. The right to life and to personal inviolability is therefore affected by the waiting times."
http://www.bluecross.ca/
Supplementary health plans for individuals, families, seniors and employers of all sizes continue to be the specialty of the Blue Cross Member Plans. The plans provide supplementary health and dental benefits, including prescription drugs, vision care, semi-private & private hospital rooms, short and long term disability, emergency medical travel, ambulance, home nursing, chiropractic and life insurance.
http://www.fasken.com/web/fmdwebsit.../$File/PRIVATEHEALTHINSURANCE.PDF!OpenElement
Contrary to myth, it is only provincial legislation, not the Canada Health Act, that prohibits
private insurance contracts from covering medical services that are funded by medicare.
Aside from Quebec, five provinces (Alberta, British Columbia, Manitoba, Ontario and Prince
Edward Island) prohibit private insurance from covering medically necessary services. The
remaining four provinces do not.
The existence of these restrictions pre-dates the Canada Health Act. The Quebec ban was
introduced in 1970. Ontario has prohibited private insurance from covering publicly-insured
health services since 1969.
If private health insurance was of genuine concern to successive federal governments, then the
Canada Health Act could have been amended to stop the practice. The fact that six provinces
already impose their own bans should be immaterial; after all, four provinces do not prohibit such
private insurance, and an ostensible goal of the CHA is to maintain consistent national standards.
Some argue that the Canada Health Act creates a practical barrier to private insurance of
medically necessary services (at least in provinces that still charge premiums) because provincial
health plans must be run on a non-profit basis, making it difficult for private plans to compete.
An additional disincentive is that doctors who receive fees from the public health care system
may not "extra bill" (that is, charge prices exceeding the medicare rates and seek private payment
of the difference).