Not true at all.
If you’re using hot water from a tank it’s possible to use all the water in the tank and have to wait for it to reheat, but a tankful of water should be enough for several long hot showers. And most showers nowadays heat their water on the spot, so they’re limitless.
I wonder if he has confused memories of seaside hotels from about 50 years ago, where you might have to put money in a coin-operated electricity meter, and if you didn’t have a coin of the right denomination you couldn’t get hot water.