I think you got that backward. The general placement of college football programs in the rankings over time is more dependent on player talent acquired through recruiting. Obviously though, recruiting better talent is a neccessary but insufficient condition for success.

Lou Holz could never bring a national championship to my hometown team of William & Mary when he coached them in 1970 and 1971. But he did bring one to Notre Dame.

And I like to use UCLA as an example. Long considered by many to be a generally underachieving program, UCLA has nevertheless won about 75% of their games against BYU.