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Evidently not, as foreign doctors aren't allowed to immigrate to the US and practice medicine without first going through a costly and onerous relicensing program. As it stands, all foreign doctors, even from first-world nations with statistically better health outcomes than the US like Germany or Japan are all deemed unqualified to practice medicine in the US: http://www.nytimes.com/2013/08/12/business/economy/long-slog...
The real question is why programmers should be singled out for this kind of treatment when US doctors are the highest paid in the world, price-per-procedure is the highest in the world, and medical bills remain the number one cause of bankruptcy.
Further, a global workforce is only one component of free trade. What about a global retail market? Did you know that there is presently a federal law barring the re-importation of prescription drugs from nations where they're sold for pennies on the dollar? That form of free trade is bad for the bottom line of big corporations, so it is illegal.