I was wondering the same thing, so I did a quick search...
Osceola County allows you to buy alcohol beginning at 7 am, Monday thru Saturday. On Sundays, sales begin at 9 am at liquor stores, gas stations, and supermarkets, and 11 am at bars and restaurants.
In Orange County, you can purchase alcohol in liquor stores, gas stations, and supermarkets starting at 9 am, 7 days a week. In bars and restaurants, sales begin at 11 am.
From what I've read, most of Disney World falls under Orange County (I'm not 100% on this, so please correct me if I'm wrong), so maybe that's why people are having trouble getting alcohol early?