Look at the instruction sheet provided with the Equalizer hitch.
Unless I misread, it recommends lubrication for the L bracket and the top of the spring bar receiver to reduce noise.
It also recommends keeping the bolt holding the spring bar receiver tight.
You don't put grease on surfaces where you want friction.
You don't have tight bolts as a pivot when you want to pivot freely, either.
The other issue that may cause confusion is that springs are not necessarily coiled wire.
check the diagram at http://www.equalizerhitch.com/home.html
and note where the arrow by "friction sway control" points. or check the faq which says "The Equal-i-zer hitch eliminates trailer sway through a friction system built directly into the hitch head."
Let me know if you think I misread the Equalizer instruction sheet and I'll go back and re-read it again.