It seems weird to me when mafia mentions those as an unpermed skill of that class before I ascend when it isn't also mentioning things like hodgman's skills.
It's going by skill numbers.
Seal Clubber skills are 1000-1999
Turtle Tamer skills are 2000-2999
...
Accordion Thief Skills are 6000-6999
---
Holiday Weight Gain is 1024.
Jingle Bells is 2025.
...
Cringle's Curative Carol is 6027
... so, KoL itself classifies the Crimbo skills as "class" skills.
Similarly, Käsesoßesturm is 4023, which is in the Sauceror range.
Regarding Hodgeman's skills: I'm surprised. I've permed all four of them, so cannot easily test, but I don't recall anything strange about them.