Remember that once the recruit takes athletic money from the school, the school can’t give its own FA (without it counting against the team total, so why bother?). If a recruit from Duke has a 1/4 scholarship to play lacrosse, but also would have qualified for need based financial aid from Duke, that FA is gone. Recruit has to pick, athletic aid or need based. Recruit can still get a pell grant or SEOG, but that SEOG better be in line with what other non-athletes are getting from Duke (same EFC).
Now if this recruit had no need at Duke, and then says to Harvard ‘I need you to reconsider my aid and really need to get to 1/4 the COA’ Harvard is going to have to justify awarding FA in that amount. Need based only. Can Harvard do that? Sure, it uses a different method to calculate need than every other school. It cannot ‘find’ need for 1/4 the COA just because the recruit is getting that at a peer institution.