When is a Wrong Green NOT a Wrong Green??

Where you are going wrong, is that you are thinking of the word "double" in "double green" as meaning two greens. But a double green is not. It's just a single green, shared between two holes and which therefore has two flags. It might help if you think of it as a "double-sized green" instead. See Bobmac's answer for those situations where, for some reason, the committee want to regard it as two separate greens.

So relief as regards "wrong green" was not necessary. But you could have taken relief from GUR if the "other" hole was on your line of putt.