As they drive away in their heavily damaged armored truck (Langdon hit a tree as he peeled away from Vernet), Sophie wonders if Vernet was really trying to be loyal, or just wanted the Grail for himself.
This brings up a good question: who can be trusted? The Priory's obviously compromised, so they can't very well bring them the keystone.
Langdon realizes they need help from an expert on the Priory and the Holy Grail, but one from outside its ranks.
And he knows just the dude: Leigh Teabing.
Sophie is dubious of Langdon's plan. She's not sure they can trust Teabing not to turn them in, or worse: steal the keystone and try to find the Grail himself.
Langdon thinks Teabing can be trusted, and will be mostly motivated by their valuable information on a subject he's obsessed over for years.
Plus, he owes Robert a favor. (Langdon served as a corroborative expert on Teabing's controversial BBC documentary about the alternative Grail theory.)
At least money's not a factor: Teabing's loaded. Plus, he has some healthy animosity towards French authorities, so he should be willing to bite his thumb at any of Fache's attempts to capture Langdon and Sophie.
Sophie thinks Teabing's attempts to disclose the truth about the Holy Grail might present a conflict of interest to that of the Priory.
Langdon solves that by deciding Teabing doesn't need to know the full story…or that they're in possession of the keystone.
Sophie finally relents. Langdon's excited for Teabing to tell her all about the alternative Grail theory.