Such things as signature on delivery are at the request of the shipper. If ZZP requested it, and they didn't, then it is all on UPS. If ZZP didn't request it, then part of the blame lies with them.
I know every box I've ordered from them has required a signature, so I doubt ZZP just didn't do it that one time.
Also, TDC will get nowhere with UPS. Claims have to be filed by the shipper.