A Grapnel Gun using Batman & Catwoman on the other hand, could get the move from the Grapnel Gun, then get a free close combat action from it and also get their own Double Pounce Duo Attack

DOUBLE POUNCE : Batman and Catwoman can use Leap/Climb. When Batman and Catwoman are given a move action, after the movement is complete Batman and Catwoman may use the Duo Attack ability as a free action.

If you want to get really ridiculous, turn them to +2 stats and flurry on the UB with lt gordon on the team. Once clear, power action gordon to grapnel gun, duo, flurry, then flurry again as a regular action.

Actually it does say give this character a move action to do a specific effect just in not so many words. The use of the semicolon and colon indicates cost and effects directly tied to said cost.

That semicolon right after action indicates that everything listed after is a direct result of giving this character a move action to activate this ability.