Interesting! If Lacroix says "they're," that indeed suggests he orchestrated the encounter, because he has knowledge Nick doesn't and is sharing it in that remark. If Lacroix says "your," that suggests Nick coordinated the encounter. If Lacroix says "the," motivation is neutral or at least undisclosed.

Because I had heard "the," I had always thought the trio came into this particular tavern by coincidence, with no foreknowledge of the musicians. If I had heard "they're," I would have made the same construction you do. Rot Lacroix and his evil machinations! ;-)

I wonder if the captioner heard "their" (same as your "they're" to the ear), knew that was wrong, but amended it in the mistaken direction, to the other possessive? I do not hear particularly well -- which is why I read captions in the first place -- so I'd be perfectly content to learn that the "the" is really "they're." Besides, it would reveal more about the backstory!

I love new-to-me FK thoughts. :-) Thank you so much for playing with me so often!