From my understanding of 501©(3) law, that is correct. It seems that most American professional sports leagues have a central fund that fines are channeled to, and at the end of the year the league makes charitable donations from the fund.
Where the money goes to is different from sport to sport. Apparently the NBA doesn’t disclose where fines are donated, although the fine fund is split 50-50 between the league and the players’ association for charitable purposes. The NFL has a handful of charities they have traditionally funded (I am taking this article at its word), and MLB seeks player input on charities.
It’s my understanding that international sports don’t necessarily donate fine revenues to charity. The International Cricket Council does not, for example. (The fines are usually a percentage of match fees, which are a pittance anyway.)