I award you zero points, and may god have mercy on your soul.
What school you're at does matter. Prestigious schools attract the best talent. Less prestigious schools with most or all of their money in distance can buy good talent. Less prestigious schools with no or low scholarship money in distance are going to lose.
If what school you are at made no difference then we wouldn't have this thread talking about where the coaches were moving to. They'd all pick a school, stay there and they'd all win.
I could name countless coaches who sucked at one school but succeeded at another. They didn't become a better or worse coach overnight. They were in better or worse situations.
Correct, great coaches will find a way to improve and succeed no matter what. However, there are limitations. In recruiting the typical kid can't look past school prestige (unless when scholarship is in play) just like in coaching searches some of you tools can't look past name recognition of the coach or the school they are currently at.
As for your example of a great young coach. I think you're fudging to look elitist. However, if that case is real and he coached 5 AA in six years he didn't get a big job for reasons other than coaching ability.