They are from Toronto. Would that make a difference? Their mother-in-law has had a horrible time getting referred. But I asked the same thing you did, why not get another doctor?
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.
Toronto. It likely is a problem in Toronto, especially if you haven't needed a doctor or haven't been in the city that long. Specialists ,I don't know. It might depend on what kind of specialist. Some are in short supply. And we middle aged old farts aren't helping things much by getting older. :)