Banner was wrong in his understanding of the mechanic functionality of time travel.
Its really that simple, and Steve doing what he did is the proof.
1. Oldman Steve is not the Steve we watched, he is from a different timeline, and his arrival 70 something years ago created this Branch. Our Steve who left to take back the stones, created many other branches, and lived with Peggy in one of those, and we never see him again as a young man or an old man.
(Or... )
2. Our view pivots, and we start following a different universe for the last 5 minutes of the movie. Some new Hulk we've never seen before trying to recover some new Steve who we have ever met before, who is trying to take the stones back is never to be seen again, because he's off in a new timeline, however Old man Steve is our Steve Rogers who we followed for ten years at the movies, and this is the new branch, the last 5 minutes of the movie, he created to live with Peggy in.
3. How Banner explained the rules, it's impossible to return to the timeline you started off in, except they seem to do that effortlessly, unless, they really-really don't know what they are doing and want to eat their cake and have it too. The obvious fix for this is that the platform they land on and take off from, is a beacon/homing device, and they can all travel diagonally in time to get back to it, no matter what they do to the past of another branch, and however far from home they stray.