Exactly after the fact you saw them steal a series. Not arguing it doesn't happen, but you sign contracts and manage your cap based on what you expect to happen in the future. You shouldn't pay for what someone did over a short series of games, but I'm fully aware it happens all the time. We're stuck with a bad contract with MAF precisely because of what he did in a couple of playoff series.
But analytics is about what are you going to do for me in the future and looking it at coldly without emotion. We have a fanbase that is emotionally tied to MAF forever now and if it came out that George McPhee told him "Hey Flower, we love you and thank you for what you did, but the analytics suggests our extension offer to you should be 2 years, $3.5m per because you are getting up there in age after all and we aren't sure you can repeat that performance" what would the fanbase's reaction be? And he would be right and should have let him walk because some other GM who is not good at analytics and simple strategy will be like this is a guy who has won Cups and seems still good enough, we'll pay him $6m per or more and then the VGK fanbase will be like you idiot McPhee, how could you let him go for nothing.
I'm not trying to say anyone is right or wrong, I'm just pointing out the critical thinking and strategy skills that can be improved upon by every team. Its easy to say mistakes were made looking in the rear view mirror. I accept those, but what I'm less accepting of is continuing to make mistakes or doing things like thinking if you do one thing right to correct something you did wrong, it makes the wrong go away. Signing Lehner to a fair contract doesn't make the wrong of an overpriced and probably over lengthy extension for MAF go away, and it also makes a huge strategic mistake of spending too much on a category of players that other teams can and will be better at spending much less on.
As for the proof, there have been dozens of articles written even by non-hockey focused people talking about how goalies are overpriced because it is just solving for a math problem. Save percentages adjust over time, but if trying to predict the future you have to assume the math you have predicts best what will happen. If a goalie is going to face about 30 shots a game and a series is likely to go on average 6 games, a goalie with a save percentage that is 0.1% higher will save about 1.8 more shots than the lesser goalie. Many of these extra goals will have no ultimate impact on the series, but they could. And the natural bias of fans is to remember when they could have.