Yes they do. It happened to my wife, after she was in a car accident. I took her to the nearest hospital (which, incidentally had only one person sitting in the waiting room), and was told that they didn't accept her insurance, and she'd have to go somewhere else. We ended up driving another 20 minutes to the next hospital, which did take her insurance (and had >20 people waiting for care).

All systems of health care have their up-sides and down-sides, but having lived with (and used) both the US and Canadian systems, I'd much rather have the Canadian system.