Double-click is an action-function which is comprised of hitting mouse button 1 two times in quick succession. The client does not have a shortcut for performing this action, hence the GM’s reply.
The Ctrl, Alt, Shift + Key combos are allow, as far as I’m aware of, because you could just aswell keybind the shortcut to one single key, instead of a combination, as such it does not give you any particular advantages.
Key-combinations is only a way to give you more “keys” than the usual 108-ish you physically have (excluding any special keys) on your keyboard.