That's actually incorrect. The SEC had to step in the Thursday before the game and conduct a conference call between the two at TN's asking because LSU was standing its ground and refusing to reschedule it (a third game rescheduled that year). That's how the game got moved to Monday.
The Tigers, however, opted to wait and the SEC offices had to step in that Thursday before the game and move the game to Monday. UT had offered to host the game with LSU as the home team and this had dragged on enough that UT was just about ready to forfeit if LSU didn't reschedule (Hamilton stating they would do such "if we felt like it would be unfair to our student-athletes and not safe for our student-athletes."). Tennessee was even willing to go down the day of the game (noting that it made no sense if they were sending people out of Louisiana). TN's coaches also even tried to push for the game to be at the end of the year.
LSU's AD repeatedly sited logistical concerns (after moving the first game to AZ State and their 2nd game to later in the season) and eventually it had to go to Slive and the SEC front offices- as UT appealed to the SEC offices and the situation still had not been resolved - to overrule that and of the SEC front offices had to move the game to Monday that Thursday before the game. LSU's AD even said prior that they were not going to move this game to another location. In fact, the associated press reported that LSU officials would have preferred (/ were pushing) for the game to still be that Saturday (or even Sunday) with Hurricane Rita looming over a post-Katrina Louisiana.
(LSU's AD Skip Bertman even said before the weekend that the change caused them to face significant logistical challenges and that they would have preferred to have just played the game that weekend. He states their preference to play on Sunday night if not Saturday night, and then noted to the associated press that LSU wasn't going to move the game to another location / hadn't been considering doing so.)
USATODAY.com - Rita shifts LSU-Tennessee game to Monday