Populations vs. individuals. I think that you can have ridiculously smart/talented/productive students at any undergrad or any medical school as a product of circumstance. But, when you take the bell curve of that amalgam of attractive traits, it is shifted to the right at the 'better' schools. If you wholesale replaced one medical school class with another you will notice the differences in student quality. But, when it comes to selecting an individual for a class, what school they come from means little compared to the other things on their application, whether it be for medical school or residency.
How does the specifics of a medical school affect this? Because those are the alumni that they populate their residencies, junior faculty positions etc. from. They are also the future alumni that end up in academia across the country. Prestige is built over time and while they do not sweat losing an individual, you bet that they chase after the top top students as a group. And if HMS can be more 'secure' because of their stature, all the other schools are going to work harder (though I have no direct evidence to show that).