To put this list in perspective, AP started weekly rankings in 1936. Rutgers was basically the equivalent of a I-AA level team. Even when the school went "bigger time" it took them until the 1980s to have a I-A program. Up until the 1976 undefeated season, they only managed rankings in the 1958 and 1961 seasons. And Rutgers pure football scholarships didn't even start until the latter half of the 1960s.
And counter to all this, schools like Princeton and Yale were on the football decline when AP rankings began. But if there had been such rankings since the start of intercollegiate football, they would have been occupying the #1 and #2 slots on the list.