Reborn applies Iron Fist to the same moves as the canon games only. Iron Fist doesn't boost CC in the main games, so it doesn't in Reborn.
The ability is supposed to be for "punching moves" only (ex. Focus Punch, Thunder Punch, Comet Punch), and that holds true for 95% of the moves that get boosted, though it does also include Hammer Arm, Ice Hammer and Sky Uppercut (and whatever Melmetal's move was again. (One Bulbapedia search later: Double Iron Bash))
I'd assume it's because CC doesn't really specify punching only; it's more of a move incarnation of brawling someone entirely?