Actually, this is something of a misnomer. Saban was never known as a great disciplinarian at LSU. He just recruited high character kids. Once Saban's recruits start coming in, things will turn around. Saban is known as a disciplinarian because he yells and screams a lot. But, he is also known for wanting to give second chances and caring about kids that have issues (see Damien James situation). He really did not seem that hard to me.
LSU won the NC in 2003 because of players like Marcus Spears, Michael Clayton, Chad Lavalais, Marquise Hill, Corey Webster, and Kyle Williams. They had high character players who led by example. It was the only year that the team really came together and it made a difference. It will probably take a while for Saban to build that at Alabama (took 4 years at LSU). But, once he does, it is really positive.