Immediately after training, you don't have to "drink"; drink at once and a lot (more than 0.5l). You need to drink, but in small sips and gradually (it is better to drink 0.5 liters of water for 15-30 minutes). Moreover, the water should not be cold (because the body is warmed up and weakened, and the risk of getting problems increases). Maybe this is what they mean when they say "no drink"?
To be honest, I have not heard this. If we are talking about a power sport, training in the gym, fitness, then drinking water is mandatory. Perhaps in other sports, for example, in athletics, it is limited at some stages of preparation. But this is already specific. Without water, you lose energy exponentially, blood thickens, etc.