We are?
Each province administers it's own health care but it is regulated by the federal Canada Health Act. Ontario has a payroll tax, paid by the employer , on a payroll of over 400,000 @1.9%. (Under $400,000 @ 0%).
I'd suggest your friend get a different doctor. I can see mine simply by making an appointment . And when I see him will depend on the reason. Today if necessary. I have a friend who made an appointment week before last, saw his doctor on last Tuesday, and has an appointment for a MRI on June 9th. Maybe that's slow by private standards ,I don't know.
For all the maligning the US HMO system has taken, I've had great service from mine. I recently had an MRI as well, and got the appointment one week from the time I requested it, on the day I requested it. That is almost unheard of where I live. MRIs are so backed up, they have to do them 24 hours a day. Healthcare, I guess no matter where you live, depends on your choice of primary doctor.