Upon repeated viewings, it's obvious Cap was wrong
I went full circle on the arguments regarding liberty versus morality with this movie.
At first view, no doubt I was firmly in "Team Cap" as his argument about people being subject to people with agendas resonated with me. I felt he was right about acting when you see something going wrong, regardless of those who urge caution. It was a bit of "the lesser of two evils" kind of reasoning. Sometimes, that argument is the right one.
Upon the next viewing, my mind started changing. By the third viewing, I could clearly see Tony's argument in a greater context than merely the "man against the world" mentality that Steve often employs. What I had initially viewed as Steve's stand for individual choice of action, revealed itself to be an act of self-righteous defiance, hardly a just argument. Even the morally compromised Black Widow asks Steve quite bluntly "Do you really want to punch your way out of this?" The fact that Steve's answer is "We fight," shows his personal hubris. This was the moment he lost all moral standing. Had he merely stood down and gone with Tony, they would have discovered that the real assassin was framing Bucky Barnes but NO, Steve had to have the last word and get his way. It went completely by Zemo's script. The key moment where Cap/Steve realizes he's been played is when Zemo tells him "I studied you." Zemo knew that Cap was a one man army and figured how he'd react.
So Tony was right all along, maybe not entirely in the way he thought but certainly in his "greater good" frame of mind. Steve's written apology is not very remorseful about his role in everything and again magnifies why he's so wrong. All Steve is sorry for, is not telling Tony about Bucky killing his parents. Hardly a moment of gallantry for Cap, considering the damage his decisions caused to property, Rhodey Rhodes and the Avengers team.