In 1961, it wasn't the ubiquitous plan that it is now in Canada, and varied widely depending on which province you lived in. It is the provinces that historically and individually have complete control over all health issues. Furthermore, even today only about 68% of costs are picked up by the health care systems in most provinces....what it was in 1961 in British Columbia (north of Seattle), who can say.
And just as an FYI, my mother (U.S. citizen) last year had medical problems while visiting Nova Scotia and was charged exorbitant full fees (demanded in cash!) for several treatments and a hospital stay because she was a non-citizen. Free.....HA! If it's not free today, it certainly wouldn't have been free in 1961.
For you conspiracy nuts, SURE....she could have lied, she could have snuck across the border in a jeep through the woods, faked a local address, told them she lost her Health Card and all other documents, had the delivery, and then skidaddled with the kid in the middle of the night. Yeah, right.
And one more thought: in 1961 they didn't give credit cards to students or the unemployed like they do now. She would have needed lots of cash to fly, drive and pay for the delivery.
Of course Ann was presumably a penniless college student, but her family was not.