that machinist is smoking crack if hes saying that no material on the boss of the valve seat is acceptable. If you run such a cylinder head, the valve seat can dislodge, come out, break off and completely destroy the engine in a second. (its called dropped seat if you want to google it) The green areas you highlighted are called the fire ring sealing surface and they need to be chunky too - no erosion here and equally solid on the block otherwise the headgasket will fail once the engine warms up.
the red circles I made in the picture are the actual machining limit markers provided by the manufacturer on all cylinder heads (its almost standard practice except for some engines - and on those you cannot machine the head at all - e.g. Toyota MarkX heads - read my post about the VVTi timing codes.)