When they need her for something, they both reason with lies.
Booth deals in charm, which is a lie, because misleading is legally the same thing as lying. Brennan lies to herself: Caroline doesn't doubt Brennan's a very capable professional, because she's seen her in action and couldn't understand a thing, but for all that she's about proof and scientific findings and not taking leaps of faith, her feelings interfere with her outlook on a case a hell of a lot more than she lets on.
When they ask her to prosecute something unprosecutable at the time of asking, she scowls and she pokes and she lists every reason why she would, in all fairness, be better off not doing them any more favors, but she already knows she's going to say some semblance of yes before all four of their combined feet have stepped past the door.
She doesn't know why she trusts them to make their lies into truths, to carry out their promises even when the initial case report is just this side of blank.
In all fairness, though, there are worse people she could make exceptions for.