Purely out of curiosity what makes you think they can play basketball in January when you can't play football in September? Indoor sport during the winter. You could argue a longer, more prolonged exposure to your opponent. I suppose the only thing you have going for you is the number of people you'd have to monitor.
I just think once you've put it out there you have too much liability to play, you aren't playing again until there is a marked difference in potential harm. And that's not going away by January.
If a basketball player were to get seriously sick the very first thing they'd point to is not being very far removed from canceling all football. You've basically acknowledged the risk is too high-- good luck coming back from that one from a liability perspective.
IMO the biggest difference is the NCAA dictates the basketball cash and gets little or nothing from college football cash. The NCAA will do everything in their power to have their basketball season (and more importantly) their tournament.