The whole deal was off the records (e.g., Saul tries to find out something from his guy in the office (a confidant of the president?), or as Dar Adal tells to Saul). The main point of the deal was that there is only one copy and this copy belongs to Saul/Dar Adal (Also, do not forget that Haqqani promised not to assault any US facilies (anymore ;)).
That said, the CIA (or anyone else) does not know about the deal and will never know. (To answer your question, the deal was accepted since they did not know about it. It was Dar Adal on his own who did this within letting anyone know (expect for Saul and Carrie in the end)).
In my opinion, the motivation for such a deal twofolded:
People (both, the polical leaders as well as high ranked people within the CIA like Dar Adal) want to get rid of Lockhart as head of the CIA (He is being blamed for the assault on the embassy).
They also want to have someone else in charge and to make sure that he/she stays there for a longer time and have no outstanding debts. Do not forget that the CIA seems to be weak after the 12/12 attack at the end of season 2 and the incident in the embassy.
The video would be such an outstanding debt and could lead to problems in the future if Saul becomes CIA director again.