The truth is that it all depends on two factors: How much you ate and how hard you intend to swim.
Fear of Drowning
The concern that prompted this maxim is the fear that somebody who has just eaten could get a stomach cramp if they swim right after eating. Getting a debilitating cramp could cause you to double over in pain, and if you are in the water, this could mean that your mouth and nose are under water.
If it’s severe enough, the cramp pain could cause you to be unable to straighten up and theoretically you could drown, although this is highly unlikely under normal circumstances.
Meal Size Matters
Most people won’t get stomach cramps after eating a small to medium sized meal, such as the size you probably would normally eat while having fun on a summer afternoon.
If you were to eat a huge feasts — such as a Thanksgiving dinner or another massive meal — then immediately try and exercise vigorously, the likelihood of your getting a stomach cramp is much higher.
How Active Will You Be?
Another consideration is how vigorously you intend to swim after eating. If you simply plan on standing or playing normally in the water, the risk of a cramp is low. But if you dive in and start swimming laps as quickly as you can, the chances of cramping increase.
The depth of the water is another consideration. If you are able to stand in the water easily, unless you suddenly have a massive cramp you probably will be able to remain with your head above water.
But if you are in deep water that is over your head, even the smallest cramp can become dangerous.
The best advice is that your mother gave you: Just to be safe, wait at least 30 minutes after eating before getting back in the pool!