No, that's not true. It gives you a plus when you score in certain situations, and a - when you get scored on in certain situations, and it's not very well tied to an individual player or their abilities.
We needed top 4 defensemen. Period. Regardless of what you think about Barrie, it was undeniably an improvement on our other options going into this year. Defensemen also aren't just "offense" or "defense". Barrie provided elements other than production that we lacked, and had been exploited, like an ability to exit the zone from the right side instead of just endlessly icing it.
But it used to be the Capitals, which you mentioned, and they didn't play that way when they won.
His team is alright defensively, but they do give up a decent amount of quality chances. No team wants to spend endless amounts of time in their own zone. That's a horrible strategy.