"Cool, what's that look like?"
The Dashing Hero is doing something during the camp that allows them to copy a move. Rules As Written this is not a multiclass poach and as such disables starting move chains that would all be required to work together, like Born of the Soil - Studied Essence - Shapeshifter or Spellbook - Prepare Spells - Cast A Spell.
But given that there's nothing in the rules stopping them from picking up Ritual under these circumstances, it seems like ultimately the real barrier is the feasibility of why and how the Dashing Hero can pull off the copy in the first place.
Of course, it'll be up to the GM how it actually comes off. Here's what I think is reasonable:
Cleric/Wizard: Cast a Spell. The Dashing Hero has no caster levels, and so can prepare rotes (minus any spells that are rotes because of cleric or wizard racial features) and a first-level spell that the Cleric or Wizard could prepare. Unlike the Cleric and Wizard, they cannot break for an hour to reprepare forgotten spells.
Cleric: Divine Guidance. This one's interesting. Can the Dashing Hero believe in the Cleric's deity? Do they follow a faith of their own, but never gave its god or gods anything that they might be repaid? It could break either way.
Druid: Shapeshifter/Spirit Tongue. Interesting for the same reason as Divine Guidance. Can the Dashing Hero understand the Druid's land? Do they discover a deeper connection to their own native soil?
Ranger: Command. It's probably a little more sensible that the Dashing Hero can also work with the Ranger's animal companion, circumstances permitting, than that they temporarily cow some passing wild creature into doing a couple of tricks and vanishing.