There are schools who have two week rush periods but most of them are 1) not SEC competitiveness level 2) you don't have to wait for a week to find out your invites for the next round.
I think they're trying to make it so women don't drop out of the school if they don't get a bid since that did happen when all of rush took place prior to classes. It is a good idea in theory, but the actual execution is somewhat less than stellar IMO.
ps: If she was spoiled, she wouldn't have listed the top sorority at the bottom of her list. Although you can also remind her that having 3 groups left out of 8 makes her, simply by math, more awesome than some of her HS friends who rush at Bama and Auburn, are in the same stage of rush, and have 3 groups left out of 17!! Yes I know this is not exact math but it sounds good.