Floor moisture issue, discoloration. What could be the cause?
So you must realize that although there is no standing water anywhere on the ground below the floor there is moisture (a vapor). Concrete can be thought of as a sponge in that it will absorb moisture (water) and allow it to move through it.
Most concrete slabs have a plastic vapor barrier (sometimes) installed on the ground, but not always. If the wood floor was glued to the slab and moisture is transferring from the ground this is what is causing the water stains and there is no easy fix.
On the plus side the wood is not swelling (looking at the photo's) and the staining appears to be limited (although it's hard to see). Perhaps a darker colored floor stain would hide the marks. Is the wood becoming loose or warped?