I can't speak to what sources you were reading, but the air under a hovercraft is higher than ambient air pressure, not lower.
Hovercraft use blowers to produce a large volume of air below the hull
that is slightly above atmospheric pressure. The pressure difference
between the higher pressure air below the hull and lower pressure
ambient air above it produces lift, which causes the hull to float
above the running surface.
Here is Wikipedia's image of a hovercraft:
If this craft weighs 500 kg and has 2 square meters of area, it would need a pressure of ~2500 Pascals to hover. Atmospheric pressure is ~100,000 Pascals, so the hovercraft needs to be few percent above atmospheric pressure to work.