Nope. You're wrong.
You can't at all say that for subjects like lit or poly sci. Those are subjective subjects. Math, science, and engineering are not.
Having top notch research facilities in order to attract big talent is irrelevant to the conversation we're having here. Undergrads aren't doing big budget research. We are talking about undergraduate education. Having or not having a particle accelerator at your school doesn't determine how well you will learn elementary Calculus.
US News, mass surveys, and the Shanghai rankings are also irrelevant to this conversation. Those are ranking universities not undergraduate programs (yes I'm aware there are rankings for undergrad programs but that's not what you have provided). Furthermore, they are surveys. Surveys are opinions not fact nor scientific. If you even bother to read the criteria of these ranking systems, you'd see that there is very little if at all anything to do with ranking the actual education and ability acquired at these schools.
Your running analogy makes no sense. A more sensical version of your failed attempt at a relevant analogy would be "some teams are harder or easier to get on than others, but your actual success in improving is not very dependent on which team you get on". That is correct.
Your problem is that you are confusing or refusing to separate entry standards, prestige/reputation, and the actual education. Two of these things are dependent on where you go. The other isn't.
Your suspicion is incorrect. I've attended and currently do research at one of these high ranking programs.