The problem is that if you sign for it, they can later send you the bill.
Not sure that they can do here. I used to work in order fulfilment for BT and deliveries were often disputed. All we could do was send a disclaimer for the customer to sign that they hadn’t received it and they got a free phone. I tested our courier with a parcel sent to my home. The consignment was logged as signed and delivered even though I wasn’t in, and when I got home there was a card through door informing me that the parcel was left at the butty shop across the road.