Of course it isn't only based on R&D dollars. But if Washington and Stanford both thought they could ****hole-conference-backdoor their way into playoffs and/or control the conference like Texas did in the Big 12, that would have absolutely factored into their decision to apply or not.
Fact is, Stanford and Washington are far, far better schools than USC both in terms of athletics and research. If they had applied to the Big Ten, they would have been welcomed with open arms.
All of that said, research is king. Big Ten schools often get more in NSF research alone every year than the entire athletic conference distributes amongst members. Academics is king and the regents of the vast majority of schools in the Big Ten understand that. Athletics is a feather in the hat that can help attract people to a more complete package of a school.