This post is unrealistic in medicine, and really only works for less serious/elective care issues, not primary medicine, or where doctor and location choice actually matters.
As a starter: I'm woman with an extremely strong family history of breast cancer before age 50. Standard clinical guidelines is to start doing heavy monitoring 5-10 years before the youngest person in the family tree was affected, since usually cases get progressively younger start dates. Since one of the people was around age 32, I'm under the age of 30 and I go for mammograms, ultrasounds, and MRIs every year as if I were a cancer patient already.
Mammograms, ultrasounds, CAT Scans, MRIs, (any form of medical imaging radiography) are actually a perfect example of how the market internationally could be more efficient, but it turns out that's impossible. At its core we're basically talking about photographs, something facebook manages to serve from location a to person b that is nowhere near location a every day. Why couldn't I go to any imaging place in the US, and have my images sent to the lowest cost provider somewhere in india to be read and interpreted by a radiologist, and then have the results sent back to me. Unlike Chris, I don't even have to meet my doctor, all I have to do is send him images.
It turns out that medically this is blatantly difficult if not impossible to do. The reasons are 2 fold
1) It turns out that age and variations in how and why the machines that used, as well as technician speciality, matters a ton in image quality.
http://www.kevinmd.com/blog/2010/09/mri-places-good-quality-...
As a patient, I have no idea if the price I am being quoted is reflected of image quality or price inflation (and this is before being read)
2)Quality of the radiology report is highly dependent on the MD reading the images. This has been well studied since the early 2000s (one of the latest examples being here: http://www.ncbi.nlm.nih.gov/pubmed/23737538 ) At under the age of 50 with dense breasts, I'm significantly more likely to have imaging misread if I went into a community imaging location, even if they had top notch equipment, because the radiologists do not have enough volume of high risk cases to make sure I am not falling into false positives/recall on a regular basis - which would mean even more imaging costs.
In order to effectively export my images, I would have to find a way to duplicate part of the specialized cancer wing I go to. Cost savings actually would be minimal - I'd be running more tests, seeing more doctors, and probably have a delayed diagnosis if/when my expected inevitable happens (which means more expensive drugs, longer treatment times, ect)
And while my example is specific to me, many people have similar sorts of conditions where treatment location, equipment used, and people involved have higher initial costs but lower lifetime costs for all sorts of conditions. Pretty much any semi-serious disease falls into this category.
I'm game for better ways of paying (insurance does cover this, because as I said, lower lifetime costs to them by paying for preventive care). I experiment with things like telemedicine - I use a compounding pharmacy and Specialized RN over the internet to manage acne that refuses to go away. I'd totally go to the Caribbean for teeth whitening or LASIK.
None of these things need regular, serious followup, or run risks of painful drawn out deaths/longer painful medical care with much higher costs if done very incorrectly on a regular basis.
Medical tourism isn't the answer - understanding what these services are in relationship to risk is.