It is the movement of the tyre bead, valve, etc as it rotates. Some pressure in, some out, along with a bit of osmosis. The tyre is not a perfectly sealed environment. The bead and valve stem move as the tyre rotates and heats up. Moisture that gets into this area can be drawn in by the movement of the bead/rim interface (most tyre beads are angled, along with the rim). Same if you do not run a valve cap, moisture can sit in the valve when stopped and be drawn into the tyre. Same as the rubber valve spins around and moves and the surface between it and the rim can draw moisture in.
We are not talking a lot of moisture/water, but then you don't need a lot to create a saturated environment.
With earthmover tyres, as most haul roads are watered, you can put a tyre onto a brand new rim and remove it 18 months later and the combination of moisture in the air and an elevated temperature will have corroded the internal metal surfaces of the rim - but the external surfaces are fine. This is on a tyre with a bead width of 4" and an operating pressure of 110psi cold and 135psi hot. The rubber expands and moves and this can draw in moisture like any capillary action through a very small or microscopic opening.
The liner itself is also not totally impervious to leakage. For this reason, liners exposed to chemicals or even sunlight for too long can embrittle and become porous - but this normally leads to mechanical separation. In earthmover tyres, this can lead to a major tyre fire.
Craig