I disagree that Hainsey "pinched" in the conventional sense of that term. He had a clear assignment to cover Kopitar in that situation. Even if he had backed off and remained at the red line, he clearly should still have been fronting Kopitar as long as he was a threat for zone entry. Whether or not he steps up on Kopitar has no material impact on the outcome as long as his teammates maintain their own assignments.
The thing is, if you look at the play that Kopitar made there, he knew exactly what the Canes were doing defensively. He knew he was man/man with Hainsey, he knew there was a forward coming back to cover for defense. He created a vacuum and set up his teammates to play a 2-on-2 with a forward covering. What he might not have known, in that split second, was that the forward was a rookie who was in the process of making a major positional error which would transform the 2-on-2 into a 2-on-1.
Observe:
[nhl2]c-48819003[/nhl2]
As he crosses the red line, McGinn is fixated on looking at the puck. He's hustling back so it's understandable that he's got his back turned, but critically he doesn't pivot into a defensive position at this instant when he has the chance. Therefore, he's stuck in tunnel-vision mode rather than having a full view of the ice to diagnose what's happening. He gives Doughty a quick glance, then focuses on the puck.
Doughty has now crossed the ice, left to right, to fill the vacuum that Kopitar created. Because McGinn didn't pivot when he crossed the red line, he's lost in the play. When he tries to find Doughty in his old position, there's only empty ice. For a crucial half-second, McGinn keeps floating over to the right wing rather than going into emergency "you've lost your man, dummy, so skate back hard and pivot as you cross the blue line" mode.
In the video it gets obscured by the Fox-box, but this is McGinn's "Oh ****" moment. Having lost Doughty, and having at no point pivoted into proper defensive position, he's coasted all the way over to the right wing without an idea of who his assignment is supposed to be. The freeze-frame above is the exact instant when he first lays eyes on Gaborik, hits the brakes, and attempts to stick-check him just to slow him down on his clear path to the net.
The line change had nothing to do with any of this. Kopitar and Doughty ran something that looks an awful lot like a set play, taking advantage of the Canes' man-on-man defensive scheme to create a vacuum, and McGinn completely misread the situation -- at least in part because of a lack of rigor in his physical positioning and not having his head on a swivel. This is what we get when we leave a rookie winger as the high man on the forecheck against three All Star caliber opponents.