Your source says "athletic departments", not football or basketball programs, which is an important distinction. Football and basketball are the only money-makers (I think hockey or baseball make money at a few schools), and all of the other sports drag down the athletic departments budget.
That's also ignoring that FBS is basically advertising. There's been a steady increase in applications (and subsequently an increase in average GPA and similar numbers) at University of Alabama under Nick Saban, and I know I would have been less likely to go to Virginia Tech if it wasn't for their football program drawing me in when I was in middle/high school.
Jim Calhoun and Geno Auriemma did more to take the University of Connecticut to national prominence than 100 deans. And Auriemma did it by excellence in a non-revenue sport.
While Mark Few at Gonzaga made the NCAA tournament 20 years in a row, this small Jesuit school in Spokane doubled the number of applicants, increased the proportion of students from outside Washington, increased incoming student test scores and dramatically grew the endowment.
That's also ignoring that FBS is basically advertising. There's been a steady increase in applications (and subsequently an increase in average GPA and similar numbers) at University of Alabama under Nick Saban, and I know I would have been less likely to go to Virginia Tech if it wasn't for their football program drawing me in when I was in middle/high school.