That's the difference. By not having you sign for package, they still assume responsibility after it is left at your door. Once you sign, you have ACCEPTED the package and they no longer have responsibility if it was stolen. If it was damaged, you could send it back and they would replace because there is an actual item to send back. If verizon were to just send you a new phone after you signed, and then claim it was stolen, it would create a scam industry of people pulling that, and verizon would lose millions and they would cease sending phones out, or they would force you to pay an extra $50 to $100 for insurance.
When you sign, you're signing that you received the package not that the contents are correct.
If the box is empty it's up to Verizon to figure it out and eat the cost, not the customer.