Err... Yes! Why did you think it could do anything while in standby?
So it's not in standby then. The most direct evidence of whether RTS is up and running is the response of WebIF to scheduling a recording (or deleting a recording schedule).
Interaction with the RS web service is by the HDR-FOX
rs package polling the web service; the web service can't reach into the HDR-FOX. If you want to make ad-hoc recordings via RS, you need to leave the HDR turned on - otherwise RS will be waiting for at least the half-awake state for the HDR to download any new instructions. Even when on, it only polls RS every ten minutes (as shown on RS by the "last seen" time).
Things Every... (click) section 18.