IMO, Murray isn't a pusher at all, he's a versatile "grinder". I know these terms have no concrete definitions and I've seen them occassionally used interchangeably, but IMO there's a difference.
Murray grinds - yes he often gives himself a large margin for error, and yes he's often getting the ball back seeking to invite errors from his opponent (believing that he's more consistent), but he's also "working" the point at the same time to create opportunities for himself to be aggressive - get a short ball and put it away, or get a look at a passing shot, or get himself to the net.
He doesn't just put back all fluff. He hits forceful shots, even if not completely ripped, he runs his opponents with his hitting patterns, even if he's not usually going completely for the line. He is trying to force errors, but at the same time he's trying to open up the court for himself to take charge of a point when he can. I don't think the slow balls he does put back changes that.
Pushing is more desperate and much less varied, involving literally just getting the ball back because there's not much more the player can do. Murray can do a lot more and he does.