Can't speak for other countries, but from Canada the answer is - they don't. It's US folklore; fake news, if you must. I have lived 30 minutes from the US border, and 2 hours from a major US city for my entire life - I can't name one person who has done that, and can name plenty who could afford to. For our area, the closest major city IS actually in the USA - so in some cases it could make sense for travel distance alone. Example - for flights and concerts, I usually wind up in the US, simply because it's much less driving. But still - can't think of one person who has gone there for medical reasons. Definitely know some people who have brought pets there for vet work, as there is more competition and it's less expensive.
That all said, I know there are some that do, and I could see there being instances where a specialist has more experience, and/or more capacity in the US. You guys have 10 times + the population, which definitely has advantages in areas like that - be it monetarily advantageous for them to set up camp in the US, or simply that there's a larger talent pool to pull from.