Flush? I think you might be overstating it a bit. Most smaller schools use their financial aid money to lower the cost of their private school tuition closer to that of the state schools. It's simple math and how smaller colleges market themselves.
Let me pose this scenario--Suppose we have a small Indiana college with a wrestling team. They are competitive, but certainly not at a level of churning out national championships individually or as a team. Who are they more likely to "recruit:"
Wrestler A with a 3.8 GPA, 1200 SAT, semi-state qualifer
Wrestler B with a 3.0 GPA, 1000 SAT, 1X state placer
Truthfully, I don't know. If I had to venture a guess I would say they probably recruit both, but Wrestler A is going to get more of their "flush" financial aid? For a lot of D3 schools, not all, sports serve as a marketing/recruiting tool for prospective students, and I think small college sports is mutually beneficial to both parties (wrestler and school).