It's not 'free'. You just have an insurance that covers for it, but you (or your parents) are paying alot for that aswell. But even those insurances varies in their models. Some require you to pay in advance and than you get it back. There are also countries without insurances though.
I don't how Canada works, but countries with public health use taxes to finance themselves and you don't have an insurance
We also have 'public' and 'private' health and it works similar as you mentioned, just as insurance and not taxes, but well...both is mandatory so it works nearly the same
Of all the things that have happened, I'm just shocked they had to pay a hospital bill for that fight. Is it because I'm Canadian and most of this shit is free here???