Not at most schools they don't. They go straight to the Foundation, which distributes.
And don't bet your nuts, unless you don't need 'em anymore.
USC is not poor in anything. They just see a better opportunity to get off of a sinking ship.

As for the "double" thing, welp, you tell me. Looks like more than double, yes?

From what I can gather, the donations directly to the football program are counted as part of a football programs revenues.
Also, a universities endowment does not = football programs wealth or power. Sure USC might have an impressive university endowment fund, but that has little to do with the football program.
USC football brings in roughly $73 million a year in revenue, which is good for 23rd place in CFB. That might as well make it a poor when you are talking about the major heavy weights of the sport. Ohio State is at nearly $140 million in revenues. Almost double USC but not quite.
That graph/chart is not specific. What is it? TV money per conference school? Or average revenue per conference school?
If it's TV money, that's what $27 million more per school? Give USC an additional $27 million. They are still like $40 million short of the total revenues Ohio St brings in. The difference is probably in....donations. Ohio St is likely bringing in a lot more in donations to the football program. Which would make sense. It's got a way bigger fan base, alumni base, enrollment base, and it's just a much larger national brand.