That is a motorcycle. Besides simply weighing a ton more, it has a lot of inertia that a bicycle doesn't, particularly in the wheels.

Another test besides no-handed is to ride a bicycle on rollers and see how much of your corrections are made with your core, and how much is made with your arms. You will feel it in your hip flexors. If you have a very smooth pedaling technique and good balance, you don't need to correct much at all, and won't notice this as much. But normal riders, especially those who haven't ridden rollers much, will definitely be making corrections primarily with their lower body.

This next part you definitely will know and not disagree with. Regardless of the body motions and physics in play, once you know how to lean a bicycle, you just do it. You don't have to consciously think about push right to go right, countersteering, tilting your hips, or any of that. Most people in fact would need to watch themselves on video to properly describe what their own body is doing at speed.