As it was explained to me, anyone can get a doc consultation with a specialist at a particular hospital or with a GP in a clinic. Sometimes it'll require a referral.
For cases like mine (that were borderline emergency) those docs would have made room in their schedule for me. I know too many of them to think otherwise. Not to mention the fact that most make room in their schedule for emergency consults. Just ask. It's not as complicated as people make it out to be. Docs, the vast majority of the time, are not money grubbing scrooges that the public wants to portray them as. And I've had a pretty terrible experience in the past with docs, so I have reason to adopt that sentiment.