You are correct.
Their request was up their chain of command. Either their CIA boss or the State Department boss chose not to respond or their second level boss chose not to command.
Based on the Congressional hearings, the woman kicked it up and the request was denied at State.
The CIA did not make the request to DOD.
The POTUS and the Sec. Def. were watching it in the WH sit-room. Why would anyone need to make a request for help?
Fact One:
1) Only the POTUS can authorize a CBA (cross border authority) command for a rescue mission in a foreign nation.
Plus Fact Two:
2) No rescue mission was attempted.
Equals Fact Three:
3) 0bama turned his back on 41 State Dept. and CIA employees refusing to issue a CBA command and went to bed so he could go to Las Vegas the next day.