> The UK, for instance, has the opposite problem, where becoming a doctor is much easier

According to a friend who qualified in the UK and now practices in the US the _process_ of becoming a doctor is much harder in the UK: medical schools in the UK test students holistically (i.e. big exams which test all the topics) whereas American students are tested one module at a time (so lots of cramming).

I agree that gaining acceptance is probably harder though (ish: the UK government subsidises the provision of medical teaching so places are also capped in the UK for financial and capacity reasons).