Water doesn’t get “electrified” the way Hollywood shows it. That said, water and electricity aren’t exactly a safe combination either.
Here’s the way it works in the real world.
If you have an “electricity leak” (typically something conductive like a wire or a pump or a light, where the insulation has become degraded somehow), what you have is 120 or 240 volts AC (or maybe up to 440 if you are certain of that voltage) at the fault, and 0 volts at earth ground (meaning literally the ground, as in dirt, mud, rock, etc) at the bottom of the pool or canal or bathtub or whatever. In between there you’ve got water.
You may have heard that electricity takes the shortest path. That’s wrong. Electricity takes all paths. However, more electricity will flow through the shortest path than will flow through longer paths. And actually “shortest” in this context means most conductive, which may or may not be the physically shortest path. More electricity will flow through 100 feet of copper wire than will flow through 3 feet of wet wood, for example.
Since electricity takes all paths, it spreads out through the water. You end up with these voltage gradients all through the water. If the voltage all around you is the same, that’s no biggie. It’s when you have a larger gradient across your body (in other words, a higher voltage on one part of your body than on another) that current will flow through your body.
If you touch a pump with an electrical short in it with one hand and you touch a metal pipe sticking up out of the canal with the other hand, now you’ve got the full 240 volts (or whatever the pump is) straight across your body from one hand to the other. The path of the electricity goes through your chest, and there’s a very good chance it will screw up your heartbeat and kill you.
If you just swim up through the water, you’ll probably be pretty safe as long as you are 20 or 30 feet or more away from the pump. Get in close, like 5 to 10 feet, and you’ll start to feel tingling. If you feel tingling, there is more than enough current there to potentially screw up your heartbeat, so get away from it immediately. At those low current levels though, the chance of death is fairly low. The closer you get to the source of the electricity, the higher the risk of death.
Like core I’m having a bit of difficulty picturing an entire family getting killed, unless they contacted an underwater high voltage line or something like that. Or if they were struck by lightning. Your typical lightning bolt is a few billion volts with a few hundred thousand amps of current flowing. You need a few hundred yards of water between you and the point where the lightning bolt hit before the voltage gradients get down to the safe level.