This link describes the sports medicine concern with hyponatremia that occurs in athletes who sweat a lot during an event, and then drink large amounts of water. Jennifer was not sweating like an athlete, but her body reacted in a similar way.
It turns out that the DJs were joking about a person who died from water intoxication two years prior to their Wii contest... so they knew it was dangerous. The radio station was sued by Jennifer Strange's family and had to pay them quite a bit. The following article from the LA Times newspaper gives the details.