What I understand from your diagram is pretty much what you said. The "GREEN" wire is serving as a "trip" for the relay to send power to the lights either from the low or high depending on which wire you choose. The way they drew the diagram it would seem they are leaving a switch as an optional item that you can add, and then show you how to do it in the smaller box diagram. They are using a lighted switch, that is why there are three wires to it (additional ground).
If you wish your lights to come on at anytime and only controlled by the switch, select any other wire on the the bike that is hot only when the ignition is on.
I think I said all this correctly.