The people are correct; no load equals little or no boost. This is because free revving the engine requires very little fuel to accelerate the motor. Little fuel equals little expansion of combustion gasses. And as we all know the expansion of combustion gasses is what causes the turbo to spool up.
However when you place the engine under load more fuel is required to accelerate the motor. More fuel equals more expansion of combustion gasses by an exponential amount. This quick increase in combustion gasses causes the turbo to spool therefore forcing more air in to the motor which in turn allows even greater amounts of fuel to be added, it’s a vicious cycle that generates boost.
The basic and simple point of it is that when the engine is not under any kind of load not enough fuel is introduce into the system to produce boost.
To answer your second question, yes free revving at 4,000 RPMs the engine is moving a lot of air; however that air doesn’t contain very much energy. At least when compared to energy released with the expansion of fuel rich combustion gasses.
Hope that helps some
