Yes. The movers consider surcharge (tariff) condition that makes them repack your items again in case they see any improper packaging, or the carton you packed your things on would harm the shipment process. Since you are in a provision of their service, the movers and packers' prime responsibility is to serve your belongings with full safety and security assurance.
This makes them liable if any accidental loss or damage would be caused during the shipment. They become liable for all this until the cause for damage falls under any of the concern law defenses like- The act of the shipper, the Act of public authority, and so on. An indecent shipment packaging is considered to be the act of the shipper. Hence, the major cause for any damage will be considered under the act of the shipper which makes the shipper responsible for the loss.