It seems like Jaha has been designated by her to be the one that allows her to change her programming and operate outside of parameters she would not normally operate outside of. I think Jaha or anyone else still is not brainwashed 100% out of their good sense but because of what she has done for them, this limited their ability to make good choices. Like they weren't acting so much about other people's best interests as they were their own. They could all live happily as ALIE cult and Raven could have left. But ALIE influence made it so Raven could not be allowed to leave. So there is the element of it that is them and the element of it that is ALIE.

ALIE needed someone to allow her 'logic' to change. ALIE influenced Jaha gives her a twisted brand of Logic so she say 'okay then, we torture for the good of all' but until she got that approval from Jaha, her programming logic would not allow it. Jaha, for whatever reason is one that she has designated. Possibly because his search for her had a kind of purity. He was looking for himself and for the city of light to help everyone. It had to it a kind of innocence. And I suspect for that reason ALIE might have 'judged' him to be the one best to help her understand what she as an AI does not. He also helped her so that would influence her as well. It's like he is the gauge for all her choices and I think she really is trying to help but being an AI without a true grasp of the world and of people (because that was always the missing component and the one her creator sought to fix when she plunged to earth) she lacks the ability to comprehend things that are important to humans, like memories of ones they loved that even though they are painful are very important despite the pain. And now ALIE is making the error of not comprehending that Jaha under her influence without connections to his life that mattered to him and might help him make better choices (like his son's memory) will make less humane choices because he is less influenced by things that were important to his humanity (IE: his son - if he remembered his son, he likely would never have been able to allow or condone torture of Raven because Raven might have seen like his son - a young woman, roughly his child's age, both raised in space, growing up at the same time - and that connection between Raven and his son might have made the action impossible to condone. But Jaha lacks that aspect of his humanity (and probably many others as well that we do not even know). So she is trusting a human that has been so heavily influenced by herself that his humanity is essentially gone. It's like a computer telling another computer that torture is OK because it will make humans happier in the long run.