I have been using an Equalizer hitch for about 14 years now. When I got the first one, Progressive said it was fine to lightly grease the L brackets along with the pivot head. They did not have the plastic sleeves yet. I have done this since then and my hitch is quiet and I have yet to experience any sway at all.
That said, I avoid adding grease to the L brackets unless I hear some noise. Even then I only add it to the head and that usually quiets things down. If it doesn't, I will put a very small amount on the L brackets. Usually have to do this only once a year. The head gets greased about 3 or 4 times a season.