In short, Biz-Nasty isn't in favor of the advanced stats. For this response, Bissonnette was lambasted by much of the hockey community (including myself) for his lack of understanding and conformity. Similarly, Patrick Roy has been an outspoken opponent to advanced stats, and has been similarly derided for it by writers (again, including myself).
So, we have some players and administrations in favor of the advanced metrics, and some against. The issue is more complex than that (considering sometimes they say they are against it but are really for it), but the question becomes: should NHL players and front-offices care about advanced stats?
This question has a few facets, the first being what the point of statistics are. Statistics serve two purposes: describing what has happened, and predicting what will happen in the future. While a set of data can't completely predict future performances, both kinds of stats can be useful for an NHL team, but they need to be used in the correct ways.
Statistics that describe what happened in detail don't have a lot of use for teams in the NHL. On a basic level, they know what happened, and that's what's important. If a team is outshooting their opponent and losing, they can probably say that they got unlucky, or the other team was lucky. Perhaps the goaltender had a bad night... whatever the case, the team already knows it.
On a slightly deeper level, there are some descriptive stats that can point out trends to teams that are helpful. If, for instance, you notice that your team is taking 5 penalties per 60 minutes of even strength play on average, that's bad and you probably want to mention it. At the same time, a GM or coach probably already noticed that they were getting called a lot and will bring it up.
There's an old Yiddish expression: "To a worm in horseradish the world is horseradish." To an NHL team, hockey is their horseradish; basic things like that probably aren't going to surprise them. In other words: trends that I or others may find through looking at statistics are inherently visible to the team, simply because they're paying attention all the time.
The real benefit of predictive advanced stats would be in identifying good players before they are drafted. While CHL Stats are being gathered, it's not to anywhere near the same extent as the NHL. In other words: while we are evaluating NHL players by metrics which have proven to be more reliable than just goals, wins, and sv%, we aren't picking players for the NHL team using those same metrics.
It is entirely possible that NHL teams are tracking shot attempts in minor leagues; the NHL is (for some reason) more secretive than other leagues about their "advanced" stats. There has been a recent influx of advanced statisticians into the NHL which indicate teams are paying more attention to numbers beyond wins, losses, and goals.
One effect of these numbers being readily available is easy to point out: as soon as a trade is made, fans everywhere point to it either as a good or bad move based on per-60 stats, or possession metrics. When Chris Stewart was signed, he was bemoaned as a waste of a traded draft pick based on his predictive stats. When Sean Bergenheim was signed, there was a lot of excitement over his possibly being a "diamond in the rough."
I didn't choose those examples by accident. There was significantly more excitement over Bergenheim than Stewart, yet who were people more reluctant to let go? This illustrates an important point about the NHL's "advanced" statistics: they are far from perfect.
Obviously there's no way to predict success or failure perfectly, but there are some major holes in the NHL's current stats. Firstly, luck still plays a huge role in generating a players' numbers. A players' shooting percentage can vary wildly from season to season (see Pominville, Jason). Which is the true player? Without a long career, we can't know, and by the time there is enough data to say for certain, it's too late to do us any good.
In the end, the problem always comes back to context. Sometimes, a stat can hide a player's flaws because of something it doesn't take into consideration, like a linemate. We've developed WOWYs (With Or Without Yous) to help isolate linemates and eliminate that problem. There is one context that there's almost no way to adjust for, however, and that is coaching.
Toronto has not had a great start to the year, but at least part of that is due to their low PDO- a rough measure of luck- which is even worse than last season's.
This coaching effect can matter on an individual level, as well. Perhaps a player's skill set is perfect for one coach's system, but terrible for another's? When Thomas Vanek came to Minnesota, there was much hand-wringing over his lackadaisical defense in such a sturdy defensive system- that Vanek seems to be doing just fine speaks to our misunderstanding both of coach's systems and how to evaluate a player's "fit."
Yet another confounding factor in the whole coaching mess is that coach's are not robotic creatures immune to change, but can adjust to make their system work for the players they have.
In short: while the stats we have are very useful for some things, there is a long way to go before we can rely solely on spreadsheets. Even if we could, that would miss the fun of the game we analyze so much.