I've watched the This Old House video on patching drywall and see where they use a fiberglass window screen or a screen patch one can buy at a Lowe's, etc.

BUT it would seem to me that after placing this patch over a hole and covering it with joint compound that it would be raised relative to the surrounding wall and thus show no matter how much feathering of the edges one does.

What am I missing? How does such a patch not show?

And better still, why even use it if I use paper tape around the sides of a wallboard patch?