There is always a strong sense of national pride in medicine. Many people both inside and outside healthcare believe their nation has the best care, and make it an institution of sorts. It really seems stupid and insignificant, but the fact that foreigners are not feeling welcome has consequences. For example, US people often compare to german docs. Except I'm from Europe and having worked in the US, I can tell you I wouldn't go back to the US even for a million bucks. Why go somewhere you do 1.5x the hours, have a miserable quality of life and be treated like s##t, just to earn a little more ? So, if the US was to open the floodgates to foreign grads, I don't think the 'brain drain' would go the way people expect.
Within the US, the limitation of admission of US students into med school is another matter. And I think people are probably right to call out protectionism in this case. But I have no first hand experience, being a foreign graduate myself.
I'm just a random bloke having worked in Boston, though. So YMMV.