Actually, it's not true to say that "greens are dominant over fairways".  Different renderers processing OSM data will use different rules, but a common one is "draw smaller areas over larger ones" which lead to the effect that you think you're seeing.  
However, if something is either fairway or not green it does make sense to have them as non-overlapping, as https://www.openstreetmap.org/user/CurlingMan13 has now edited it.
