Here's what Cox has told me:
When a Court issues a valid subpoena requiring Cox to disclose the
names of customers who are suspected of illegal activities (executed
via misuse of Cox High Speed Internet service), Cox has no choice but
to comply with this subpoena and provide the Courts with the requested
information, including customer names.
Cox is in full compliance with the Digital Millennium Copyright Act,
"DMCA". Pursuant to provisions of the DMCA, when Cox receives a valid
notice sent from an entity claiming to be the authorized copy write
holder, Cox then notifies its customers who may be illegally sharing
copyrighted material that they are may be in violation of the law. Cox
also notifies its customers who do not promptly desist from illegal
file sharing that their services will be suspended or terminated, as
required by law.