He's wrong, he was probably in a rush and having you check is wasted time for him. When you sign it you're signing to say that you've accepted delivery and the items were in good order. We used to sign everything to say they were unchecked but even that's not good enough now.
You're well within your rights to open the package and check the contents before signing for it. It's at that point you sign it as normal, damaged but accept and then contact the vendor or refuse it and mark it as damaged. If you receive a parcel that is damaged visibly never ever sign for it before opening it and checking it, and even then sign for it as damaged in case the product doesn't work when you come to power it on/use it.