Where did you hear that? I live in Toronto, which has a constant shortage of family doctors. In fact, most Government reports I read, indicate a nation-wide shortage of family doctors. He's a psychiatrist so he was booked within 2 weeks.
My experience with the Canadian healthcare system has been poor. Our system is designed to catch and treat the big killers (cancer, heart disease, trauma). And in those cases, it does well, once a person actually gets treatment (iow, long wait times). For other non-life threatening conditions (mental, hormonal etc), support is terrible.
Socialized medicine is not all it's cracked up to be. Cost and waste is enormous. My friend says there's so much abuse and waste in the system that could easily be eliminated, but due to the nature of bureaucracy and no oversight, nothing changes. While everyone receives care, it's mostly substandard care with long wait times, unless you're on your deathbed. A great compromise is a two tier system which runs parallel along side each other (public/private). Many affluent Canadians travel to the US or abroad for superior medical services that simply aren't available here because Canada outlaws for-profit medical practices.