I think college’s ranking do matter in Med School apps. The key is that you don’t want to get into a school way below US News 200. In my state, California, there are VERY few CSU students got into med school (other than Cal Poly grads). I think those local non-directional grads have a low chance to be accepted by med school.
For fun, I was looking at a school called USAO (in OK) web site because it has a very low COA
Well, a student made to OKU SOM was posted on the front page and was named Honored Alumni.