He didn't suggets Boucher only has one system. He actually said the opposite in that Boucher has mutliple systems (even if they all suck). Hard to argue that great goaltending wasn't the reason we made the playoffs and the reason we made it as far as we did once at the party. Andy most definitely made this team look better than it is during last year's run.
I went back and watched it again, he said theres no way you can convince him that Boucher only has one system. So you are kind of correct, where he is wrong was that he was suggesting Boucher only uses one and should adapt. It may come as a surprise to many but he does have more than one NZ system. Look no further than tonight, they often sent two forecheckers, The Dumont goal was a result of a heavy forecheck, Chlapik chased behind the net and Burrows cut off Borgman on the other side of the net which forced the turnover. This isn't just a new thing either, the game earlier in the season against Toronto is another good example of a different approach. There's a lot that goes into the preparation of the games and the approach varies based on opponent and feel of the game.
The 1-3-1 is nothing more than a meme, and honestly it has more of a 1-2-2 feel. Personally I don't think the neutral zone systems have been the issue. Last year the thing that stood out the most to me was how well they protected the net. The goaltenders where good last year, obviously better than they have been to this point but last year I felt there were a lot of easy nights for them. A lot of that is how well they defended the front and the slot, it was pretty rare that teams were able to get the puck to the middle of the ice and get a good look at the net. and when they took a shot from the outside the rebound was taken care of, it was beautiful to watch. Outside of that western Canada trip and a game early in the season vs Detroit I'm not sure I've seen the consistency defending the net, they are giving up a lot of free looks and that makes it tough for the goaltenders.