I don't think Crosby is a clutch playoff performer and I don't think people that would say he is are using the same universal standards most use for the word. I think of guys like Gretzky, Roy, Sakic, Kane, etc. when I think of clutch bc its more about the timing/psychology of greatness.
Sakic in 96 for example didn't just lead the playoffs in scoring, he scored very key goals in games where the Avs were either on the brink of elimination or on the brink of going down 3-2 in a tied series. A lot of his goals were game-winners as well. He was almost like a superhero that playoff run.
I think of Roy in 93 with his overtime streak or his wink in the finals. He was unbreakable and his confidence demoralized the opposition. That reputation mythologized him in a way and he proved himself time and time again by raising his level of play once the post-season started. He was like the immovable object in that sense.
I think of Gretzky's OT goal in 88 against the Flames or his Game 7 hat trick in 93 (there are probably a lot more iconic moments that I'm not remembering). In general, Gretzky had a killer instinct and wanted to crush the opposition every chance he got.
Kane in modern times also earned his clutch reputation by scoring game-winners and seeming to rise to the occasion whenever he was needed. His overall playoff numbers weren't any better than his regular season play, but the timing made a difference.
Crosby's still a good playoff performer and was reliable/versatile but he didn't really rise to the occasion offensively in (key moments of) the post-season like the guys I mentioned(not saying he never has, but it's not often enough for it to be a defining quality). I don't see it often, but when people do bring up Crosby as a clutch player, it's usually a package argument in a grander narrative of why he's better than a McDavid/Ovi and pretty dependent on confirmation bias and team success. Saying he's not "clutch" isn't saying he's not a good playoff performer.