From what I've seen, luck (or lack thereof) was part of it, and maybe that's just my read on it but it seemed like Kloten was not encouraging the D to shoot much from a distance.
So because of it, he does not strike me as having a "shoot first" mentality. He's quite patient at the blue line and you can tell that he's analyzing the play in real time. However, when he shoots it, it almost always goes through traffic.
I'm not going to argue for all games as I did not watch every single Kloten game, but Reinbacher definitely played PP1 duties towards the end of the season, at least in the games that I watched. I remember being frustrated at Ang whiffing on rebounds.
It could've been an alternation between games and not a full-time assignment, but he definitely did. Apparently even his teammate Faille came out on French media to say it.
It could've been because the EJ-Peltonen duo went cold for a bit. Also I'm not saying he had all the O-zone starts but he did have a bunch.