Except that Sage, Quinn, and Riona said it is JUST a rumor. So, I gotta agree with them and disagree with you as its clearly stated several times in the narrative.
So, if as you said, if someone other than Quinn or the HOTs are the ones spreading the rumor, then how can it be "an external rumor spread to mess with them" if there actually IS a tuition reimbursement program? If that were the case it wouldn't be a rumor, it would be advertising. You talked yourself out of your argument there.
Heather was talking about HOTs paying their dues. She's a sister. She's not an officer. She doesn't have privy to the finances of the frat, thus Riona's reaction in that scene (who, being a coconspirator, is fully up on the finances better even than Sage is). Heather doesn't know what's going on behind the scenes. Sage and Quinn do and they think they have money problems. I must disagree with you and agree with them as it's clearly stated several times in the narrative.
The HOTs money problems are the entire point of the conflict of Episode 5 (they cancelled on the DIKs to go to the A&O party because they need the money. Sage flat out tells the MC that over the phone. And Sage and Quinn argue about it during the car wash, and Tommy and Quinn fight about it at the end of the Episode. I recommend you go back and view those scenes. I gather you may have skipped through them.
I agree with you that Quinn needs money but there is no indication that she is being embezzled...certainly not that she "the victim." From what it appears (based on what has been said and shown in the game), she's just making bad "business" decisions buying more product that she is able to sell, and it's impacting the HOTs because (more plausibly than she's being extorted) I believe SHE is embezzling funds from the HOTs. That's more in line with her criminal characterization, and the conflict as presented in the story so far.