To my knowledge MSAR only publishes data about applications, which is pretty useless.
The best data I saw on this came from an in-person presentation my kid and I saw while during an admitted student visit to ND’s science college. Not sure where it came from, but the data was just what you’d expect. HYP, Williams and some other LACs, Hopkins, Penn, ND etc. were the top producers of med school admits on a per capita basis. As I recall, ND’s production numbers were surprisingly strong – like top 5.
But basically exactly what you see from the HLS data. Kids that are able to get into competitive colleges are very similar to the kids that get into competitive professional schools. But plenty of kids also get into competitive professional schools from other types of colleges – just not as many. It is surely more correlation than causation.