For decades it was 100% based on NIH research. It was only recently changed to give any weight to non-NIH funds. This change is what catapulted certain schools up the rankings last year (e.g. shooting NYU up to tied with Stanford).
The original idea is that NIH research funding is a direct measure of current grant-winning, field-advancing investigation being done at that institution, and that it's appropriate to say this is desirable and makes an institution "better." Non-NIH funding doesn't necessarily reflect anything related to winning grants / having a bunch of leading labs, but as of last year, is apparently also part of what they think makes an institution deserve a higher rank.
In reality, nobody who references US News ranks really cares about various funding levels, they care about reputation and are using ranks as a proxy. Truly picking what med schools to apply to, or (god forbid) deciding where to attend based on NIH/non-NIH funding metrics, would be about as reasonable as choosing your undergrad based on which school song you liked better.
