Oh, I think I understand perfectly… If you change equipment in the collection manager, it does not affect any parties already created. I’ve written quite a lot about it, how equipment is party-specific (and I’m not the only one), and these questions arise periodically.
From what you describe, if the equipment in question was not available when you built the first party, then it would not be there until you opened that party and put the item on C’Thun as a member of it. Another thing: playing ‘C’Thun solo’ actually refers, in game terms, to a new party (containing only one merc), with its own — again, party-specific — equipment.
I believe anything else to say would already be self-repetition, but, just to be specific in relation to your particular example, I would suggest that you open the original party, select C’Thun there, take a look at his equipment and ensure he’s got the right piece, then test it again in the field if you’d like to.
(Updated: typos corrected, some minor edits made)