I was going to post the rule for two reasons:
(1) Art. 2(a)(2) makes it clear that basket interference occurs if the ball is touched while any part of it is in the cylinder. So if you look at just the LSU component of the play, the shot shouldn't count.
(2) BUT, UK may well have committed goaltending before that point based on Art 2(a)(5). One UK player has his hand through the bottom of the hoop hitting the inside of the rim (he doesn't touch the ball so 3 doesn't apply) causing the rim to move, but it's very hard to tell if the ball was on the backboard when he was contacting the rim. But a second UK player slapped the backboard, and it does look like he did that while the ball was on the backboard.
Attachment 9063 Attachment 9064 Attachment 9065
Sorry these are so dark, but the video I have dims when you pause it. The first two screens are taken with 1.0 showing on the game clock attached to the back of the stanchion (I cut it out by mistake when grabbing the screens). That frame is pretty much the moment the ball contacts the backboard. The third image is taken just after the ball has already come off the backboard. There's 0.9 on the clock in this frame, and you can see the UK player's hand just coming off the board at the same time the ball is beginning it's downward trajectory after hitting the backboard.
Of course, I don't think I've ever seen Art. 2(a)(5) enforced, but if we're being technical about it, UK goaltended before LSU's basket interference.
Now no one needs to feel like they should feel bad for Kentucky.