It does seem like he is leading the quest with all the information that I have to work with. He understood the rune to make the door open, and based on the information, it doesn't seem like Thorin has done anything, really. It also seems like Bilbo has more experience with the stuff that has happened so far.
Bilbo understood the rune, and Thorin didn't.
This is just based on the information I have, I'm not sure if Thorin did something or not.
