The best answer is he makes the big saves on the big stage and his save percentage in the playoffs shows that to be true. The entire Kings team overachieves in the regular season and really I can count the amount of stinker games Quick has on one hand.
It's called team effects. Remember when Vokoun/Luongo would get peppered in Florida and posted ridiculous numbers? What happened when they went elsewhere? How about Ryan Miller this year, worst team in the league to a Stanley Cup favorite?
I had this argument all year with people before the Olympics but they've all mysteriously disappeared since Ryan Miller. It's not a science, but you can't just take one goaltender from one team plop them somewhere else and expect differently. In regards to the shot numbers specifically, I forget where it's found, but Quick's sv% goes up with more shots and we have a better win% when outshot IIRC. And I will say unless a goaltender is getting a shutout, those low shot numbers mean low save percentages when you let in one/two goals on 20 shots rather than on 30 (I know, duh, but when you have lower-than-average shots against..).
Most goaltenders will tell you they love workload, it helps keep them in the game. Quick is a guy whose biggest weakness, imo, is focus when he gets bored. How many games this season did we dominate play on one end then get scored on on the opponents single rush of the period?
Quick will likely never win a Vezina while we are a powerhouse team. His best year was when he carried us kicking and screaming to the playoffs when we didn't deserve it because he had to be in every game.
I'm pretty sure the talking heads will agree that when the games matter most I don't want anyone other than Quick. This year, Varlamov can make his case as Rask did last year. But I still take Quickie.