The offensive coordinator who replaced McElwain threw the ball too much. Alabama wanted to get back to a more physical style, especially while breaking in a new quarterback. Kiffin at Tennesee nearly upset Alabama on the road by pounding the ball at them, even though his quarterbacking was terrible. Only blocked kicks saved Alabama in that game.
Saban undoubtedly remembered that game and was impressed that an outmanned team nearly defeated him as a double digit underdog. He thinks he can take the best of Kiffin and get rid of the weak spots, like the obsession with flanker outs once he had the great receivers at USC.
I visited the USC boards today. They were mocking the hire but I fully understand it and agree with the concept. A year and a half ago, Kiffin had a preseason top ranked team despite significant scholarship limitations. It took quite a bit to get there, including an upset at Oregon as 16 point underdogs near the end of the previous season. Saban is wise enough to focus on the big picture, that it is a talented young guy and top recruiter who fell out of favor. You always want to take advantage of a situation in which someone is undervalued. Who cares if the bar stool types love to rip Kiffin? It's the same philosophy as stealing away Mario Cristobal, another coach who was highly rated at the end of the 2011 season before being canned not much later.