The clay soil usually has a low organic matter content. So bringing mulch, grass clippings etc. does improve several key factors for the plants to thrive. The problem with putting a layer of rotting grass/weeds on the top is that at least in some locations it will make a perfect slug/snail farm. So I prefer to burry it in shallow pits/trenches. Also probably any preferably dense plant cover protects the top layer from being backed by the sun and becoming brick-like.