The former is a question worth pursuing if the latter has any chance of happening.
Here is the Capitals' former goalie coach, discussing why he was let go last summer, as quoted in Katie Carerra's autopsy of the Capitals for the Washington Post:
"Adam did not agree with how I coach, both in my methods and the content of what I coached," Prior said from his home in Ontario. "My inflexibility was perceived as ignorance or stubbornness, but I perceive it as a much deeper knowledge of the position. . . . I have no regrets. I would do the same thing again because I stand up for what I believe in. I would gladly defend a goaltender and what I believe is the toughest way to play goal and lose my job over it than to pour gas on them or give them what I believe is bad advice."
Holtby's numbers (.915 save percentage) unquestionably took a dip this season, although that comes with several cautions:
His career sample still isn't that big -- despite "only" playing 48 games in 2013-14, that was actually an NHL career high as he previously played 36 (.920) in the lockout-shortened 2013 season (plus 25 in the AHL at .932), and just a handful of games in the preceding two seasons.
Goaltender numbers are notoriously subject to swings from month to month, season to season -- so it's never clear how much is concrete changes in performance and approach (or health) and how much is just natural ebbs and flows. That said, the theory in Washington is that a change in approach did affect Holtby.
Carerra continued (previous link):
Oates and new goaltending coach Olie Kolzig promoted a calm, controlled style of play that allowed for deeper placement in the crease. All three netminders who started the year in Washington acknowledged the adjustments weren’t instantaneous, but the most visibly affected was Holtby.
Of course, to our earlier point, these numbers fluctuate. Holtby's season started with promise:
While he made it through October and November with a 12-8-1 record and .925 save percentage, Holtby was facing an incredibly high volume of shots (33.2 per game) in his first 22 appearances.
It finished with promise, too, according to Holtby:
"Olie and I have been on the same page since day one. He’s been keeping me sane through everything," Holtby said. "We talked about everything and we realized that I had to get back to where my natural instincts led me and we did that as a goaltender-goalie coach tandem, and I think towards the end of the season I think that paid off."
How much you want to ascribe any of this to the way the Caps coached Holtby this past season is, well, as subjective as the next hockey argument. But before taking this as a clear conviction of the Capitals' and their approach to goalies -- who tend to waver year to year like some kind of alchemy anyway -- we should at least point out that this philosophy is not unique in the NHL.
There are at least a few clubs who believe the "east-west" passing of the current NHL means goalies shouldn't be as aggressive (think Evgeni Nabokov) and should sit further back in their crease to prepare for backdoor plays and rely more on reflex saves (think Henrik Lundqvist...though obviously we are comparing styles and not talents).
Either approach has its weakness, obviously: Aggressive angles are risk to the pass, while the withdrawn goalies are at the mercy of the speed of their reflexes and reads. A top goalie like Tuuka Rask is known for being both aggressive with angles and very good at lateral and backwards movement to cover for that aggression.
Meanwhile, just the players in the position, goalie "gurus" fall in and out of favor, and it can be as much coincidental as "A led to B." The legendary Francois Allaire fell out in Toronto amid some bad goaltending performances, only to see the Leafs goalies thrive after he left. His next stop was Colorado this year, where he is credited with simplifying Semyon Varlamov's game during what could be a Vezina-caliber season.
So the quip -- or the cry for help -- for Islanders fans who have suffered through five years of mostly bottom-of-the-league goaltending here is: Bring Holtby in, and bring his old goalie coach in just to be sure.
It's not that simple. (It's never that simple.) But Holtby is a promising target, if the Caps make him available. But like most of the masked men, you never know just quite what you're gonna get, and for what cost. As garik16 said in the recent three-year projection of some goaltending targets:
[Holtby] projects as a .915 over the three years, so slightly ABOVE average. He's had a "bad" year this year, but odds are that's fluky, and even then he's been NHL average. And at age 24, he's not getting worse that fast. That said, Washington got a bounty for their last goalie traded (Varlamov), so they may want a lot more than what Toronto can ask for in Reimer.