Using the hitch for a ground is why you see good ole boys going along at night with their trailer lights flickering, dimming, flickering etc. I was taught it was a BAD idea.
Regarding greasing a ball hitch... it does make a mess on your balls when they are exposed to your clothing or whatever and it seems to collect dust and grit (not a good thing) when left exposed to the environment when the trailer is parked.
What to do?
Either buy ball covers or make your own out of tennis balls. If you take a utility knife to an old tennis ball you can make a good ball cover. If you attach a good piece of light rope or light chain to the cover you can use it as a lanyard to keep the tennis ball/cover attached to the tongue of the trailer. It will always be right there when you need it. You can put a loop of cord through the tennis ball to use as a handle for pulling it off and not handling it too closely as it can have lots of grease in it after a period of use on one of your greasy balls.
Even if you elect to NOT grease your balls, you might want a ball cover.
Pat