Although he did mention concerns about customer privacy, it appears Verizon is equally worried about what other responsibilities they might be asked to take on. After all there are a number of illegal activities that certainly involve at least a small number of Verizon customers. From child pornography to illegal online gambling to fraud, the possible activities other industries, not to mention government agencies, would like to have Verizon and other ISPs keep track of seem nearly endless.
It shouldn't be any surprise that Verizon isn't ready to upset their customers to appease content owners. In early 2003 they unsuccessfully fought to keep subscriber identities related to RIAA subpoenas private unless the recording industry organization had a court decision in their favor, at which time they would be willing to disclose the personal information behind the IP address.