That's not true at all, at least in my experience living in Canada. You can go to the doctor whenever you please. There are certain procedures they aren't supposed to do because they aren't necessary.
They got rid of yearly medicals where they would run a bunch of blood tests even if you lacked symptoms or reason to be testing it. If they think there's something actually wrong with you, a blood test is no problem, and is done. But there's very little reason to send people for blood tests when from all other accounts they are perfectly healthy.
But if you actually have something wrong with you, or even a medical concern you want to ask about, you can just book and appointment, or walk-in to a local clinic or the emergency room, depending on the severity. There's also other options like a nurse hotline to answer your medical questions. Call up a 1-800 number and you get a registered nurse to talk to about your concerns. They can tell you if it's worth going to see a doctor, or if you should just take an over the counter remedy so we don't waste the doctor's time.
Also, it's worth pointing out that with a system like they have in the US, some people with lots of money have lots of choice and can see a doctor whenever they want. However, the vast majority of people are not that well off, and actually can't possibly afford the care they need. Their waiting time is forever, because they will never be able to afford the care they need. They can either choose to get care and go bankrupt in the process, or fore go care and hope it clears up on it's own.