I don't think funding is at all an issue. Most athletic departments do not make a profit, and why is that? It's not because they can't, it's because they choose to put all those funds right back into the athletic department. Alabama has been running a profit of 20 million+ per year, compared to a deficit per year for Auburn. That's 20 million per year that could be spent in putting the Alabama athletic department that much further ahead.
So, I don't see a problem at all. If Alabama spends more on the basketball program, at worse, at worse, there's less of a profit made, which is not the real priority of a college's athletic department. If someone like Marshall comes in and demands a renewed focus on the basketball program, I fail to see how that could possibly be a problem.
Yes, there's Title IX, but they could still invest an additional ten million per year in the men's basketball team, without any Title IX issues and without running a deficit. To give you an idea, that's enough to fund the entire athletic department at Western Carolina. Besides, it's not like the additional investment is likely to get 0 return, it's one of the best bets you can make because there's actually some college basketball programs that out earn some of the top college football programs. The only way they get into trouble is if they start far out spending their revenue, but at this point they'd have to work hard to do that.
Edit: I'll add one other things, the Koch brothers can match Alabama's spending that much is true, but they can't match the other things that Alabama has. They can't match Alabama's attendance (their arena, built in 1955 seats 10K), they can't match Alabama's recruits, they can't match Alabama's exposure. Ironically, they could be what Alabama needs and give Marshall leverage to insure Alabama invests fully in the program, but there's no doubt he'll get a lot of things at Alabama he can't where he's at now.