They can if they are pushed or extended away from the body prematurely. Some of those clips that RD posted earlier... IMO what you are seeing is hand movement that is caused by body movement, during the phase that some refer to as "connection". They are not yet moving/extending away from the body. That is still in line with a "tight hand pivot point" and doesn't preclude TTB.
My point is, hands don't move on their own, there has to be something pushing, pulling or extending them. Which is a point I've made quite often, why so much focus on generating bat speed with our hands/forearms with TTB. They are just extensions of larger muscles which should be our major power source in a swing. Do I believe the hangs get the knob pointed in the right direction, absolutely. Are the hands used to help dictate direction, without a doubt. Do the hands and wrists help control tempo.. I think so. I'd consider them a pressure gauge, they are the lever ready to release an explosion into the ball. But the force that builds the pressure is the larger muscles of the body.. at the end of the day I know f#$% all, , but that's also an advantage for me, I am open to a lot of different perspectives regarding the "how it's done".