When you draw the polygon for a fairway, you are saying that absolutely everything within that polygon is a fairway. So even if there is a green in that fairway boundary, you are saying that it is a fairway as well. Both a fairway AND a green at the same time. The purpose of a multipolygon is to say everything within that boundary is a fairway EXCEPT any "inner" relations of the multipolygon. And yes, roughs should be drawn correctly and tagged as multipolygons as well.
I'm guessing you would probably agree, but just struggle because a tool you use doesn't handle them properly.