Isn't Elena in charge of KG's legal department? It seems unlikely that operation "frame Kane" would have started without her approval. I don't see how any relationship can be built on such a foundation, and Kane really should have reached that conclusion soon after meeting her in the prison.
The Board doesn't need her approval, even if she is one of the founders of the Karlsson Group, she still has to obey the majority of those who voted for a decision...As far as I remember, Alessandra was in charge of the operation to organize the false accusation of Kane, but of course the Board was aware of what was going on...In any case, a person locked up in prison is much easier to negotiate with than someone with freedom and independence.
Besides, this special prison is one of the mandatory steps of the whole rehabilitation program, and no one ever gets into JF without passing a small but important testing phase in prison beforehand. At least this is definitely the case for men.