The AP is not bound by any rule to pick the playoff winner as their Champion. They do though because it's normally obvious.
But you wanna know how we could still have a split Natty? Just look back to last season...imagine 13-0 FSU is left out of the playoff and then they beat Georgia 63-3 instead of what actually happened.
The AP could easily vote that 14-0 FSU was their NC. It's a lot less likely now with a 12 team Playoff, but with a poll that has the power to create a split NC if it decided to and has an immeasurable influence on playoff committee members, it's irresponsible to dismiss it as meaningless.