The Wires inside the cable are insulated, however you are seeing the wire braiding that acts as a shield for those wires. I doubt it is acting like an rf shield like coax cable but it does serve a purpose. ANYTIME a cable of this sort starts to open up it needs to be taken out of service and replaced.
No the phone does not have to be present nor the Seriel# just bring in the bad cable show them, they will hand you a new cable adn keep your broken one