RTH isn't connected to video signal range at all, only controller range. Failsafe/RTH will kick in any time the Phantom doesn't detect a control signal, whether it's because it's out of range or because you switched the controller off. FPV range may or may not exceed controller range depending on your equipment and flight conditions...I've seen many vids where FPV feed recorded on the ground manages to capture failsafe kicking in even though the video signal is still intact.
Note: if you're using Groundstation on your Phantom then flying a mission with that will override Failsafe if the Phantom goes out of controller range.