Murray does his part, but he's not the HOTS or anything (by that I mean the literal acronym, not Parker). Most teams aren't going to react too quickly, which is why Murray has been played by worse defenders than Green has so far. Most coaches gameplan to stop Green from shooting, and if they do it right, they can stop him with a bad defender if that defender plays disciplined D. However, a Green that posts up, takes guys off the dribble and fires good passes requires a better guy.
In 2013, Green was checked by Steph until Game 3 when he dominated Curry on the boards and beat him up on screens. It forced them to switch Klay off Tony, because their first option was getting wrecked on both ends and eventually went out with injury. A similar thing has to happen to give Murray favorable match-ups. Sure, he may be good enough to score regardless, but that's a different debate.