Stanford has just 7,032 undergraduates. Grad students really are not part of the athletic program anywhere, and in Stanford's case involve a lot of night school MBA types (it's a cash cow). They also have a Med school. So lets go by Undergraduates. I charted out private schools. The first group are AAU FBS schools. Then AAU Ivy League FCS schools, then other FBS private schools. The most similar school in term of enrollment is Wake Forest. In terms of endowment and resources only Stanford, Northwestern, Duke, Notre Dame in FBS have more financial power. They rank even ahead of USC, Vandy, and Miami.

The enrollment argument has some validity. They probably need another 1,000 undergrads to sustain a top level FBS program. Overall they look like a 'tweener. More resources than any G5, but not the size needed for P5.

School undergrads (endowment)
Southern Cal 18,740 ($4.6 billion)
Tulane 8,452 ($1.171 billion)
Northwestern 8,353 ($9.648 billion)
Stanford 7,032 ($22.398 billion)
Vanderbilt 6,885 ($4.1 billion)
Duke 6,562 ($7.9 billion)
Rice 3,879 ($5.324 billion)

Cornell 14,315 ($6.8 billion)
Penn 10,406 ($12.2 billion)
Columbia 8,410 ($10 billion)
Harvard 6,700 ($34.541 billion)
Brown 6,580 ($3.5 billion)
Yale 5,453 ($27.2 billion)
Princeton 5,400 ($23.8 billion)

Brigham Young 30,395 ($1.47 billion)
Baylor 14,189 ($1.144 billion)
U of Miami 10,849 ($3.3 billion)
Boston College 9,100 ($2.4 billion)
Texas Christian 8,892 ($1.514 billion)
Notre Dame 8,448 ($11.8 billion)
Wake Forest 4,955 ($1.141 billion)
Tulsa 3,174 ($957.5 million)

Liberty ~12,500 ($1.1 billion) // a guesstimate, as they have ~15,000 residential students, >100,000 online