Stanford is a good program, but it certainly is not UCSF, MGH, Brigham, Hopkins, Duke, Columbia, or Penn. Stanford's match list is pretty unimpressive, and I doubt it has to do with everyone wanting to stay there, because UCSF sends a lot of people out. In fact you mention Stanford matches a lot to UCSF, but they actually only match 1 or 2 per year to UCSF, usually in GI...Which is surprising considering they are the closest big program to UCSF.
Even the people who choose to stay at Stanford for fellowships, many wind up needing to do a chief year first, do a hospitalist gig for a year, or go into the clinician-scientist track. (in fact since close to 1/4 or 1/3 of residents go into that track there, a lot of the in house slots get earmarked to those people.) If you want to be a clinician scientist and you really loved the area, then I would consider it. But if you want to be a great clinician, I would suck it up and go to a more rigorous training program-->and you could choose one on the east coast where at least your family can support you through the rough patches. Just my take, but I would not confuse the glorious Stanford University undergraduate (and med school) name with the strength of the program.