I think there is a misconception that the Canadian system covers all health care costs. It doesn't. It covers a basic level of care that all residents are entitled to. Most employers offer benefits plans that cover extra services like dental, eye wear, massage therapy, semi-private or private hospital rooms, etc.
So for something like an extended hospital stay, a bed in a ward room is free because that's covered by the Provincial plan. An employer benefits plan (for which the employee pays a fee to participate in) will typically cover a semi-private room. If you want a private room you personally pay a premium over and above your benefits plan coverage.