Answer:
Depending on why they are being moved and the proximity of the two locations I would agree. Certainly if the branch is moving there is little choice if the bank has notified the renters and asked that they prepare to move the contents themselves. Those who do not respond will have to allow the bank to move the contents or have them surrendered to the state.
If boxes are at a premium and the bank simply wishes to move the contents to another branch where demand is low, that could be a separate issue especially if the new safe deposit box is hundreds or more miles away.
Proper notification and inventory control procedures should always be followed.