Well... that's what the legal cases have been trying to decide.
The telco does NOT (re) broadcast it. It provides a remote recording service. It records a copy for each subscriber then transmits that specific copy to the subscriber who requested it. It's not that different to programming your home PVR from work, except that there is a system capable of doing it in bulk...
Australian law says you can record your own copy of a broadcast program for your own replay but you can't then sell it to a third party. The single copy for each subscriber is designed to fit that definition. Whether this is an artifice or not, whether it is in effect the telco recording and selling it, are the legal questions. So far, the lower court says it's ok, middle court says not, now heading to the top of the list, the Australian High Court. If the High Court says ok, the content owners may lobby the parliament.