I don´t remember that conversation. If she says that the HOTs house was paid for alumni, I understand that means that alumni purchased the house for the HOTs the same way Rusty´s dad purchased the house of the DIKs for them, so it belongs to the HOTs and doesn´t have any mortgages. We don´t know if alumni also pay for current expenses and bills (taxes, electricity, gas, water, reparations and home improvements...) Probably the HOTs have to pay for that with their fees, not only for their own food, bed linen and belongings. A house with, lets say, 14 girls (I don´t remember the exact number of the HOTs after their hell week) has obviously more expenses than a house with 8 girls, and more girls doesn´t mean more donations from alumni, since none of the new girls is the daughter of a HOT alumni or something like that.
It makes sense anyway that Sage is reticent to almost double the number of HOTs in just a semester. It means bigger monthly expenses, a way more crowded house, and even with the fees that every sister pays, less money since they don´t get more donations from alumni.