Here's my take (through the eyes of an older American).
The stigma as I've seen it over the past 20 years or so is mainly due to the history of those Caribbean schools (well, one could go back to the Mexican schools, but their rep for better or for worse was actually better (or non-existent) before the Carib schools really sprouted) -- formed in the 70's-80's to help chiefly Americans who couldn't get into a US school. The schools used to have extremely low entrance scores and grades. St. George's in Grenada became the best known following Reagan's "invasion" of the island (under the false premise to "rescue" the Americans there). Ironically, this publicity ended up helping the school's rep, at least in name-recognition, at a time when US med school applications were increasing (throughout the 80's up until the mid 1990's). More money was pumped into the infrastructure and better profs went down there on sabbaticals, curriculum was reworked...basically the school put a lot of work into bettering itself and its image, something which surprised me. Now the school has entry scores *comparable* to some American schools, despite the more recent decrease in total American med school applicants, and USMLE pass rates and scores that are excellent.
The other Caribbean schools pretty much all also had rocky starts, poorly funded with little infrastructure/resources, but over time some bettered themselves (e.g., Ross) to also have good rep + stats. Some others are still in their "infancy" so to speak. Mexican schools also suffered from poor rep around this time partly by association and by what was perceived as poor student quality and resources, but I'll defer better explanation to someone who is more familiar with them.
Sackler in Israel never really had the stigma, possibly because it's always had high entrance requirements, has always had affiliations with/support of American schools (thus many don't even see it as an int'l school), and was originally tailored for Jews (still is somewhat) who wanted to live in Israel rather than to students not capable of getting in anywhere else.
Since the mid-90's, Australia, Ireland and UK, sprouted many 4yr (grad) programs, many from their traditional 6yr systems, and various other isolated grad schools formed (plus more started in the Caribbean), partly to soak up the extra US applicants at the time ($), partly in recognition of the benefits that older, 2nd-career students (college grads) give to medicine in the English system, and in some cases (e.g., Flinders in Aus. if I recall correctly) to help reduce domestic applicants by request of the govt. while saving the schools from bankruptcy. Because many of these were offshoots of established 6yr programs, they escaped much of the stigma factor (plus they benefit from not being seen as "Caribbean resorts/playgrounds", another original indictment against the Carib schools, since most Americans know the islands only as a tourist destination).
So... the stigma got real roots with 1) initial spurt of "last chance" schools that took students that no one else wanted; 2) the perception that anything in the Caribbean couldn't be taken seriously.
The stigma has persisted due to 1) ignorance of the improved status of the better int'l schools (there are still and always will be many crappy ones, making it difficut for most people, let alone doctors, to differentiate); 2) elitism (student A got into US, so those in country X "must" have been less qualified); 3) the myopic perception by many that the "best" medicine in the world is high-tech and where there is the most research, and thus American.
Some of #2 is reinforced because while the gap has been shrinking, the average American IMG still goes overseas because he/she is not a particularly strong candidate for US schools. Part of the cause of this, in turn, I think is that Americans are more risk averse (the circular problem: risk in going abroad -> less qualified apply -> hindered rep) and more isolationist/national-centric than most the rest of the world, preventing many strong candidates from daring to venture abroad.
I believe that onlookers typically form their opinions by lumping schools into geographical region, for example the Caribbean has gotten better rep over the years due to (at least) St. George's and Ross, but because of those that know just enough to be dangerous, the better schools still suffer from the bottom schools in the region dragging their reps down. Yet even college-educated professionals rarely know the name of the school in Grenada and if they have any knowledge of Carib. med it's a collective one or limited to, e.g., the '83 invasion. Mexico on the other hand suffers partly because...it's effectively 3rd World "ass-backwards"/"fascist" Mexico; and many think of the UK as excellent for training "hands on" or "self-sufficient" doctors because of the British history of training practitioners for field work, with less reliance on tech (maybe as a remnant of the last great Empire?). In other words, old habits die hard (...hardly die).
Having said all that, as many doctors on this board will attest, once you're a doctor few will care where you went to school. This is.. in part because no one will know unless you tell them, in part because many of your associates will judge you professionally solely based on your demonstrated competency, and in part b.c. those associates who are well-informed will know something good about (or know a good grad or two from) your school.
I'm sure some of my opinions, maybe even a fact or two, here will be disputed, so take this as just one person's perceptions/research over the years.
-Pitman