Fighting against Hydra. For Fury. Chain of command.
Not the point. Fury wasn't in the chain of command at that point.She was fighting against the establishment which she knew to be Hydra, but again, not the point - she did what she thought was right, not what she was told to do. There's no way to twist the event son Winter Soldier to paint her as an establishment puppet. She's clearly the opposite of that, especially when she thinks the establishment is wrong.