Turns out the Shouldice Clinic is not exactly what Jack Layton says it is. According the Dr. Brian Day of the Canadian Independant Medical Clinics Association, Shouldice is indeed a for-profit clinic with shareholders. It also charges user fees and people can pay to jump the queue.
Update: From the Shouldice FAQs....(don't they check into these things?)
4) How much does the surgery cost?
The accounting staff will provide an estimate of charges, once you have either been examined at the hospital, or we have received your completed medical questionnaire. Residents of Ontario who have a valid health card are covered by the provincial health care system for the cost of surgery.
5) Do you take XYZ insurance?
We deal with many insurance companies. While many companies will pay us directly, some will only reimburse the patient. In that case, the hospital would complete all paper work and have it ready for you on discharge from the hospital. You could pay for your medical services by cash, personal cheque or credit card.
Update: Just got off the phone with the Shouldice Hospital. The hospital itself is indeed non-profit, but the group practice withing the hospital is for profit, like all other group practices in the country. You can pay cash for services above and beyond what is covered by public health care.