Last I saw the tuition/R&B reimbursement # was around $10m, so that can't account for the $40m loss. But even the idea that this number is somehow inflated is questionable when you consider that UConn's tuition is highly subsidized by both taxpayers and research funds, and a little bit by the endowment. So anything the AD pays back to the school is certainly far below the actual expenditures per student.
Also it would be a big surprise to me if UConn students are receiving 40% discount on tuition. That seems well beyond anything I've ever heard at a state school where tuition remission is typically limited for the vast majority of students.
I think the tuition numbers for the athletic department by accounting is ~$18 million.
Here are the UConn cost of attendance numbers (these numbers vary depending on the source):
UConn full cost of in-state attendance = $34,284
UConn cost after aid = $21,588
Difference = 37%.
Most of the scholarship athletes are from out of state, so the athletic department gets "charged" full out of state tuition or about $57k.
Think about the math.
200 out of state athletes at $57k/year = $11.4 million.
200 instate students at the average net cost = $4.2 million.
If UConn charged the Athletic Department net instate tuition for athletic scholarships, the savings on 200 athletes is about $7.2 million/year. Remember, this is just accounting! (Note: the number of athletes on full scholarship is less than 200, but there are >200 athletes on partial scholarship so using 200 to calculate the savings is a good estimate.)
A couple of other areas that UConn accounts for things in a way that could be misleading. Many (most?) of the costs of intramural sports comes through the athletic department. And, the way UConn allocates revenues causes sports to look like they lose more money than they do. For example, Royalties, Licensing, Advertisements, and Sponsorship revenues are not allocated to any sport. In fact, about 25% to 30% of athletic department revenues (not including subsidies and fees) in 2014 did not get allocated to a sport. These revenues included some contributions, some NCAA distributions,... If you were running a business and making decisions on individual product lines, wouldn't you want to allocate revenues to each product line to better understand profitability before you decided to cut products?