Direct-mail in coverage for damage during shipping

I need to send my laptop in for repair. The instructions that came with the packaging say that "Apple is not responsible for any damage during shipping". I think the courier used is UPS. If damage did occur during shipping would it be covered by the courier or not? Would I be able to get a replacement laptop or any compensation? Has anyone had a problem with damage occurring during shipping? If so, what did you do to resolve this issue?