Actually, only the first part of the statement is accurate: more air, yes. Higher pressure, no. Only the volume is increased or decreased (spring diameter assumed to remain constant).

The effective spring rate is relatively constant over the whole suspension height range. The element that does come into play and affect the suspension behavior (comfort…) is the pistons that the air bag rolls on to upon lowering (changing the effective diameter of the air spring). The aftermarket industry played with varying piston diameters on their replacement springs. Some of them offer springs that are softer at off road height and firmer at motorway height. On stock LR suspensions, firmer/less firm rides are likely more attributable to progressive shock damper rates than anything else.