I agree that NYU is better known for the university name recognition, but I disagree with your implication that it's not a "really top school." Honestly a lot of this is CCLCM's own fault for almost intentionally hiding its program, but if you take a closer look their students match like a top 5 medical school (I would argue stronger than NYU). Not to mention it's affiliated with the #2 hospital in the country. None of this is to discredit NYU, but they simply weren't first.
But also, this idea that reducing cost of medical education will magically encourage people to pursue primary care is a joke. The only way to encourage people to go into primary care is to make it a more compelling proposition (better lifestyle, compensation, etc). You can see it in CCLCM's match list and no doubt NYU's match list will be specialty heavy for years to come.