Radio signals are in fact induced in in the cable (since shield most likely does nothing to stop it) but because of skin effect they travel on the outside of the cable - shield (field inside cancels).
Shielding basically works by two means; reflection loss and absorption loss. Reflection loss is due to the mismatch in the impedance of the shield and the interfering wave impedance. The interfering wave essentially bounces off the shield. Absorption loss is due to eddy currents induced in the shield.
Reflection loss is the primary mechanism when the interfering wave is largely E-field (electric field). Absorption loss is the primary mechanism when the interfering wave is largely H-field (magnetic field).