I knew there was something like that, and I don't believe they distinguish between players who were "cut" versus "kicked off". If you leave the school, but transfer somewhere in good academic standing, I believe it either doesn't count as much against the school or doesn't count at all. I don't know exactly how they tally it.
That's how Saban, Miles, Nutt, everyone else is going to get away with pulling cuts when necessary.
I've always said that cutting players is much worse than oversigning, but I would not be upset if my program was in good enough position to trim the fat. It's better than being under the limit and having to back fill slots by rewarding walk ons.