Lift according the Newtonian explanation.
Air is moved downwards, so there has to be an equal and opposite force.
Air is accelerated downwards: F = m x a
Acceleration is key.
Induced flow requires a greater vertical flow through the rotor therefore requiring an increased pitch angle when out of ground effect.
Flying close to the ground reduces the induced flow, therefore increasing the effective angle of attack, without changing pitch angle (collective) and without requiring additional power.
More explanation and illustration:
Helicopter Aviation
Ground effect and lift in general has not so much to do with pressure differences.
More on lift: