Oh look - it's that rules guy again.
So, as far as Disguise/Forgery and the ability's keyed to the respective kits goes, while there is nothing explicit in the book for either, on page 178 of the PHB, under "Other Intelligence Checks", are listed examples, two of which being "Pull together a disguise to pass as a city guard" and "Forge a document".
I will concede that JP using charisma in the moment made sense, as he wasn't trying to impersonate anyone, just trying to lessen his presence. Fun fact - Disguise in previous editions keyed off of Charisma regardless of it's use. Probably a better decision for 5e to make such things open ended as far as what keys off of what.
Using INT for forgery I think is made using the argument that you need to know what you're trying to forge - handwriting, seals, names, etc. Not sure if it was an "in the moment" decision by Adam or what, but the end result would of been a tie... which narratively, might of worked out the same way anyways.
Regardless, it was good having Dan back - I missed his character interactions.