Yes. When you use your muscles a lot, as you would while swimming, to avoid cramping, your muscles need extra blood flow. This extra blood flow will come from organs that don't need much blood because they aren't really doing anything. Usually organs like your stomach and intestines aren't doing much, so extra blood can go to your muscles. After eating, your stomach does a similar thing. If you have just eaten, your stomach sends signals to your brain that it needs extra blood to digest the food. If you just eat and then swim, both your stomach and muscles will be asking for extra blood. The end result is that both your stomach and your muscles don't end up getting enough blood. Therefore your muscles can easily cramp up and you'll no longer be able to swim. Obviously, if you're just casually swimming in a pool that's not deep, this isn't a concern. But, it is a concern for children and also for any swimming done in deeper water or where there is any risk of drowning if you can suddenly not have the energy to swim. Waiting 30-60 minutes allows the stomach to digest most of the food first, alleviating this problem.

Actually, what I said is completely true. Before I posted I went to verify my answer at howstuffworks.com which is an EXTREMELY reputable site, moreso than any dumb myth debunker site. As an example, the owner of the site has gone on the news and done interviews about the power outages and stuff. He explains everything scientifically. If you would like a scientific answer you can go there and read the actual facts rather than listening to a myth debunker.
http://science.howstuffworks.com/question510.htm

I also did some research before posting. But I looked for articles written by doctors. Dr. Richard Fedorak, head of gastroenterology at the University of Alberta Hospital says that it IS A MYTH. He states that the body produces ample blood and oxygen to supply both the stomach and skeletal muscles. He states that is is highly unlikely that diving into the water soon after a meal will leave someone in so much distress that they drown. He does go on to say that competitive swimmers shouldn't eat a large meal before an event because there is a risk that cramps could hinder their performance, but not incapacitate them to the extent that they could drown.