Let's do a thought experiment where we imagine a goalie who is perfect and has the ability to stop every single shot he faces. That's because he is so athletic, or so big, or because he can read shooters' minds, or however else you want to imagine the hypothetical. His skills have only one limitation, they don't apply in shootouts because shootouts have nothing to do with the rest of the game of hockey. This goalie's skill is average in shootouts and as a result his team has the same 50% chance of winning a shootout as anybody else.
The goalie also happens to be an attention seeker and a thrill junkie, who loves pressure situations. He doesn't care at all about personal stats, only whether his team wins the game or not. His team is in a non-traditional hockey market and is struggling to sell tickets. As a result, the owner wants to have every game be as exciting as possible to boost the gate receipts.
The owner has discussed strategy with the goalie, and they have agreed that the goalie will adjust his effort to try to make every game as close as possible, but at the same time never intentionally throwing a game. They decide it is also best not to tell the team's coach of this plan, since the owner is thinking of firing him at the end of the season and doesn't want the media or the league to find out that his team is in effect shaving points.
Since he doesn't know he has a goalie with super powers, the coach does not use any all-out offensive strategies that might make sense in such a scenario (aggressive forechecking, playing with four or five forwards, using cherry-pickers, etc.). Instead he plays a typical offensive system, and the team is about average offensively.
What does the goalie do in this scenario? Obviously he can freely give up goals when his team is ahead by 2 goals or more, because he can then shut the door and preserve the one goal margin. What about if his team is leading by a single goal? If there is little time left in the game, then it is unlikely that his team will score again. A shootout brings a 50% chance of losing, so if the goalie intentionally gives up a goal late in the game when ahead by one there is an even money chance that he is costing his team a win. Earlier in the game it is more likely that the goalie's team will score again to retake the lead, but nothing is guaranteed since hockey is a low-scoring game.
If he wants his team to pick up two points in every game, the goalie can't risk giving up any lead at all. There are some situations where the gambling odds might be pretty favourable, such as playing at home against a weak opponent where his team goes up 1-0 early in the first period. But give up enough goals in those scenarios and eventually there will be a game that will remain tied and be lost in a shootout.
By similar logic, the goalie can't give up a goal when the game is tied. In fact, that is considerably more crucial than allowing a goal when his team is ahead. A tie game is at least guaranteed to earn a loser point from going to a shootout, but if the team is trailing they need a goal just to force a shootout and face the prospect of a regulation loss if they aren't able to score again.
So this goalie, even if he is really daring, will probably never allow the first goal against and will most often just wait until his team scores 2 or 3 goals before he starts letting some in. He might for fun let in a goal or two early in the game against a bad team, or let the other team tie it up at 1-1 or 2-2 early in the game if he's pretty sure his teammates can score again. Despite giving up as many goals as he can he'll still probably lead the league in GAA and have a very high save percentage.
Now let's revise the scenario to make it a little more realistic. Some goals in hockey are just unstoppable by any goalie because they come on deflections, screens, lucky bounces, great setups, or shots that are simply too fast and too perfectly placed for anyone to stop. Let's assume that on average there is one goal against per game the goalie can't do anything about. These goals occur randomly and without any regularity. Sometimes the goalie goes several games in a row without allowing any, and sometimes he lets in 2 or 3 of them in the same game. How does that change his strategy, given his objective of not trying when his team is very likely to win yet still winning every game possible?
The answer is that now the goalie will essentially have to try to stop everything unless his team is up by 2 goals or more. Even if they are ahead by 2, he could end up blowing the lead by messing around and giving up a goal for fun which is then followed immediately by another one on an unlucky bounce. Similarly, he wouldn't want to intentionally let the other team tie the game because there is always the chance they will then take the lead on an unstoppable shot.
If his team scores 0, 1 or 2 goals in the game (which happens 47% of the time on average) the goalie will likely try to stop every shot he faces. If the team scores 3 or 4 goals (which happens 38% of the time on average), the goalie might let in one or two intentionally. About 14% of the time the team will score 5+ goals, and in that case the goalie can let in some goals for fun.
Multiply out the probabilities of the team's goal support with the expected intentional goals the goalie might allow, and the average would be about one intentional goal against per game. So if a goalie was trying to win every game while simultaneously never trying to stop the puck when he didn't have to, his goals against would be about one goal higher than it would otherwise be. That is, a save percentage of close to .000 when it doesn't matter would equal a GAA increase of about one.
I think it's pretty clear that under any even remotely realistic assumptions about how much a goalie is going to be goofing off when his team has the game in hand that the GAA effect is going to be very minimal, unless the goalie is playing on some kind of dynasty that is always blowing out the opposition. And even then it's certainly no positive trait in my book that a goalie doesn't care whether or not he gets scored on, even if his team is well in front.
It remains possible that there may be slight differences in team performance because of differences in goalie success in high-leverage situations. But I'm not convinced that is either significant or based on repeatable skill. If it exists it will create a slight difference between goalies with similar performance levels, but there is simply no way that a goalie like Marc-Andre Fleury (.907 career save percentage) is doing more to help his team win than a Tomas Vokoun (.917), regardless of career win/loss records.
I think the basic problem behind this common misconception is that people consistently overestimate the level of control a goalie has over his own play and the number of goals against. Vic Ferrari writes constantly about how hockey is a game of luck, and that's really true. Yet fans have heard lots of stuff about how goaltending is such a mental game, so they think that a goalie in the proper mental state can just decide to make himself unbeatable. Either that or or they give too much credence to one of those overplayed stories where Patrick Roy or somebody stood up in the dressing room and said, "Get me one more goal, boys, because I'm not letting in another one." He probably said that almost every time they were tied after two periods in the playoffs, and needless to say his team did not always win the game.
Sometimes the shooters make their shots, that's a fundamental basic truth of goaltending. It's not always the goalie's fault that the puck hits the back of the net. Anyone who wants to be a goalie or who wants to properly evaluate goaltending needs to be aware of that simple fact, or you're evaluating the luck-soaked result instead of the skill-based process.
If there exist some goals that are unstoppable and a goalie can't predict his team's future offence, which are two basic assumptions that obviously hold in hockey, there really is very little opportunity for a goalie to mess with the scoreline without costing his team. And that is why attempts to explain away poor individual save statistics with references to a goalie's win total are just biased nonsense.
Long story short, the next time you hear an announcer say something like, "It's not how many saves you make, it's when you make them", what he's actually telling you is, "I have no idea how to separate the contribution of a goalie from the contribution of the rest of the team."