No, that's word-perfect for what I've seen a Mitchells' Cockatoo do. There were two in a cage, they had no roosters around, had never seen a chicken and were both in their teens or early twenties.I'm not sure if the fake tid-bitting is in any way associated with true tid-bitting. We humans might just mistake it for the same or similar behavior. I think it is a completely separate behavior with completely separate sounds, actions and motives, and no chicken confuses the two behaviors.
I have two macaws housed outside in an aviary 24/7 near the chickens. The two are fairly strongly pair bonded although both are females. There are times and situations when the two macaws will become quite unmanageable, especially around dusk (roosting).
In the cold weather I bring them in the house for the night. These two are well socialized, trained, mature birds that I fly free outside and who are trained to do many tricks. However, if I leave it too late to bring them in the house, they become quite aggressive. The behavior is so predictable, I now will never go in their flight anytime near dusk. They both drop to the ground making a funny sound and then sidle/stomp over to me sideways with eyes pinning to attack my feet. If I were foolish enough to ask them to step up on my hand, they will bite. When they are in this mind set, I lure them outside using me as the lure. Once outside of their flight, a lot of their aggression drops and if I am able to get them off the ground, I can ask for a step up and bring them in the house and I have my pet birds back, not the monsters I had a few minutes before.
When they move in (to attack my feet), they will pick up and throw down sticks and stones. It reminds me of that scene from the original Planet of the Apes where the apes (or was it early humans?) picked up the femur bone and beat it on the ground.
Is this natural macaw behavior or is it learned behavior from watching my nasty rooster? I honestly don't know. It is new behavior (the picking up and throwing down of sticks and stones) that started in the past year since I got my chickens. I don't think I ever saw that behavior before the rooster started to attack me. Maybe the parrots quite understood that "fake" tid-bitting behavior when they first saw it and decided to incorporate it into their repertoire of behaviors to communicate with me.
He did everything you're describing. His keepers used a high pressure hose to pin him to the walls when cleaning the cage.
Also, X2 on the fake tidbitting, it's not the same, and the chooks never mistake it though I've seen them mistake all manner of other communications. I guess we can only call it fake tidbitting because we don't have any better description for it, and after all it's remarkably similar.
Best wishes.