But I don't think that is really true.
There is plenty of flexibility for people who chose their medical specialties well. And anybody's job choice has some risks.
I see an awful lot of doctors, dentists, medical techs, etc. here, that are young Americans, even though I'm in an area that had a huge influx of foreign born medical workers beginning 3 decades ago.
People can chose to go to doctors of almost any nationality around here.
My mother's nephrologist is foreign born and has been here for decades. Her GP is a young US-born woman. Her podiatrist is a US-born male. Her dentist is a young US born male. My daughter's dentist is a young US born woman. One daughter had an American born obstetrician, but found a foreign born one she likes much more.
As for the qualifications of foreign born doctors, you can check their qualifications and educational backgrounds online. You can see if they are board certified (like my mother's foreign and American born born doctors) or not board certified (like my American born male doctor).