Really? I didn't think the teams had any say so. What I remember (and those are some shaky brain cells) is that CBS had already broadcast their one night game (Bama-FU), so they had to work out some kind of deal with ESPN and the SEC to get a 2nd one. I didn't think either school was involved in the decision. Even now, if you look at the schedule, some games have a 'TBD' next to kickoff time.
The way I remember it, in this instance, LSU did have a say in the deal. They were fine with going prime time for the '11 Bama game, but stipulated that the '12 game be a Saturday Night in Death Valley kickoff. A pretty sweet deal, in my opinion.