Hurts was not hurt.
Tua is a freak playmaker (ala' college version Manziel) and fans, insiders, and coaches were calling for him to replace Hurts much earlier in the season. Hurts is a dominant rusher, who is really good at rolling right and throwing it out-of-bounds, but his weaknesses were exposed and exploited as soon as they started playing legitimate competition. Tua is Kenny "the Snake" Stabler reborn, and that's what Bama needed when UGA sold out to stop Hurts' predictable off-right-tackle runs. None of the Bama faithful were surprised by the change, and most welcomed it.
Fortuitously for Bama, by not competing in the SEC championship game, they had over a full month to prepare for the CFP. During that time, the Freshman kicked *** and the coaching staff finally convinced Saban that they were not only ready, but had earned their shot. Incidentally, Bama had 5+ true freshman playing in the 2nd half.
Despite his incredible W-L record, Tua > Hurts, and that's why he got the start when the game was on the line. Saban has been both heralded for having the guts to start Tua and criticized for not playing him sooner. Perhaps he should simply be acknowledged for making a good, timely decision that put his team in a position to win. If we could all be so rational...