the downside to this is the water will stay on the slabs it wont permeate through...
I have seen people ( me being one ! ) paint garage floors which seemed a good idea at the time but as soon as the snow or wet weather arrives the car is garaged and the water runs off and just lays in puddles rather than drain/soak away. This then creates a nasty slippery floor just waiting for an accident.
He could power wash it and then give it a coat of concrete sealer ( the stuff that they paint on to block paved drives ) it is clear. That should help to stop it getting stained.
If these are paving stones made of natural sandstone or limestone, then it happens because the surface gets dirt ingrained in it. This is removed by jetwasher, as you seem to have discovered, but it comes back again.
I don't see painting is gpoing to change this - dirt is still going to collect in the surface.