Besides general supervision, the DOD demanded a specific change from Jon Favreau's original script. An officer, maybe Rhodey, said people would "kill themselves for the opportunities he has." The DOD said that line had to go because they didn't want any reference to soldier suicide, which is kind of a thorny subject with them (even though, you'll note, that line wasn't about soldier suicide).
Favreau suggested a change to "people would walk over hot coals for the opportunities he has," and was surprised when the military accepted this. Eventually he cut the line, possibly because half that movie ended up being improvised by Robert Downey Jr. anyway.
TheTerminator's Robot Uprising Was Caused By The Military?
General Brewer in Terminator 3: Rise Of The Machines is the father of John Connor's love interest and a general in the Air Force. Higher-ups push him to activate Skynet, he does, and the machines, as the title daringly predicts, rise. He dies, but helps the heroes with his last act. The Department of Defense looked over the script, made some unspecified changes, and approved it -- also approving of Brewer himself, whom memos described as "loving."
Then the filmmakers decided to go a different route and change the general into "a negative character." And thus the DOD withdrew all support after having formally given it in writing. Did the general purposely help the machines? Was he secretly a machine himself? Did they make him into a nerdy audience surrogate who kept making meta jokes? We don't know, because the filmmakers eventually reverted to the "benign general" anyway. And so America was saved. I mean, not from the machines. They still killed, just ... everybody.