As someone who was in Greek life at the time, I can confirm this was still the case in ~2017 when the AD proposed upping the student athletic fee. The increase, if I recall, resulted in about $2.5m+ annually in additional revenue. The university student president was a Chi Omega and she campaigned fiercely for the students to vote in favor of the increase. Only about 9% of students voted, and out of that group I believe over half were in Greek Life. It was their turnout and support that got the proposal passed despite several pockets of resistance from other groups on campus who didn't see the benefit in supporting the AD.
The Greeks are still our biggest on campus supporters (aside for the Maniacs - although I would be willing to bet most members, if not all, are in fraternities/sororities).