directly to SERTC?

Here is the reason I ask. Let's say, for examples sake, that VT wrestling has a budget of $100K.
A donor gives $5K. The athletic director at VT then says he only need to fund $95K since a donor has just given $5K. He then takes the $5K that he does not have to fund wrestling with and moves it over to another sport. So VT wrestling still ends up with $100K after the donation. Is that a fair example? Or, am I wrong and it does not happen that way?

Money is fungible and it is very common at all nonprofits (like universities) to shift things around. I do see that any donation directly to a sport at VT lets the athletic director know what is important to VT sports fans. However, I just don't know if a donation through VT fundraising really gets to where it is intended. That is, to make VT wrestling better. Any thoughts on the subject would be appreciated. TIA