Well the assumption about the favours is not wrong, but don't forget during the group assignment Rachel didn't know much except bits and pieces about the founding families. And as such I would wager she either went down some conspiracy forums on the internet or is just imagining something she spun into a fanfic about a notorious partiachal cabal, feeding into her shallow ideals and/or repressed sexual fantasies.But if it's someone who knows MCs situation, then the favor is likely to be of a much more political sort, and thus far more likely to be potentially malicious, or otherwise something that could damage MC should he grant it.
Rachel is often touted as a possible thief, so the interesting question is what would make her so desperate for a family heads favor that she would steal from a man she actively hates? What would make her desperate enough to trust him?
I'm still on betting on the theory of Rachel stealing the book just to prod the MC or have him do some 'humiliating' stuff as she continuously projects her fears and desire onto the MC. I really think the whole who stole the book thing spirals out of control and people start following some red herrings that were initially unrealistic scenarios. (Following occam's razor here)