Mark, I think the reason he wants the grass gone is because it inhabits the same rootzone as the apple tree, thus depriving it of nutrients, and therefore a less-hardy tree. There are quite a few other plants that can grow under trees that don't take up that same rootzone, such as shallow growers like strawberries and deep growers like dandelions. I've been told that I should go so far as to remove all plants for three feet around the tree to reduce competition, especially around young trees (
https://permies.com/t/36743/forest-garden/Sheep-Sorrel-Apple-Tree-Seedling,
https://permies.com/t/46814/trees/Prune-Fix-Trees).
To answer Dave's question, this thread has a lot of suggestions:
https://permies.com/t/39835/trees/rid-grass-Apple-tree-guilde, such as planting comfery, rhubarb, horseradish, sweet potatoes, or lemon balm, . Or, applying a deeeep mulch, or inoculating with fungi (a nice way to do this would be to use nice leafy forest litter as the mulch.), or running sheep/chickens/geese around the trees. Another person mentioned that if you keep the grass cut short, it won't develop as much of a root structure, and so will not use up as many nutrients.
What I do--and I only have two years of experience at this!--is lay down old paper sacks, cover with forest litter or woodchips (grass clippings don't seem to work as well), and plant bush beans and peas, as well as comfery, dandelions, nasturtiums, and strawberries under the trees. I still have to pull grass by hand under most of the trees, but there's quite a bit less of it to pull, and it will hopefully soon be out competed by the other stuff.
I hope that helps answer your question!