With the aforementioned video in mind, I'd think that chickens can overcome more fencing than they get credit for, it's just a question if they want to.
I don't have the best example, but I built a small fence around my yard just to keep my birds off of the concrete so they don't poop every where. All of my chickens can easily jump to the top of the fence, and when they were smaller, go through the fence. I have a raised bed garden that is the same height, and they all fly up there every single day. However, since I have two Pekin ducks that are the "alphas" of the flock, since the ducks can't go over the fence, the chickens don't either. Even though the chickens go into the garden when the ducks can't.