The first thing that everyone who is against a single-payer, medicare-for-all system in the US points out, is all those Canadians coming to the US for health care. They ask "if the Canadian system is so good why do they come here for medical care" and they always follow up with an urban-legend like story about someone they met on vacation from Canada coming to the US for health care. They never have any stats to back it up.
Here's a Canadian study on the issue and its answer is "They're not coming here". They don't find any evidence of a mass of Canadians coming to the US for health care.
A summary here:
Phantoms in the snow | The Incidental Economist
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