sweetie,
That's not a no-frills rule. Unless of course, the sororities were competing with differently shaped ice cubes.
What I've seen on some websites is that, for example, if there are 10 sororities, the 3rd and 7th ones the PNMs go to are designated "ice water parties" so they can have something to drink, rather than nothing or having a drink at every party (I would be hopping around on one foot after about 4). That sounds better to me than having to glug down a water bottle between parties.