Continuity DOES have a value to program directors... and it's especially important if you're trying to land a job as an academic.
Of all the transitions you listed, the weakest connection is college to med school. The selection process beyond med school becomes more subjective and personalized by an order of magnitude.
At "top" schools, residency programs like to recruit students they've gotten to know who are interested in that field. It is usually preferable to retain a valuable student who they know than take a chance on someone who looks good on paper. That's why it's usually a "sure thing" for a few students applying in every field to match at their alma mater, regardless of the formalities of the NRMP. Ditto for fellowships, and for staying on faculty. At my institution, lots and lots (>50%) of medical school alumni get sucked into the Hopkins vortex and stay on for residency, fellowships, and many become faculty members.
For good or for ill, academics are an inbred bunch. If you're looking for a job in the real world, just go to the best programs you can. The job market is bright for most physicians in most parts of the country, and continuity of your training won't be as important as the strength of your training.
Cheers,
doepug