I did use a lot of hot water yesterday. I had 13 dishes to wash + the cups + the silverware. I doubt the pilot flame can heat it up that fast. It's a small lighter-like flame and it's a tank made out of metal with a second tank inside, that's where the actual water is in.
It's not when you're using the hot water, it's when you're not using it. When you start using hot water, the tank begins to heat up new cold water while still using the hot water.

I am not an expert, but I'm just going to go on the basis that heat rises and it draws from the hotter water up top first. Convection from the bottom, where the heating is, keeps the area at the bottom warm, etc.