There is a bit of confusion here. The TSR buffer is 0.ts (hidden away, I don't know how the file system works on an HD-FOX but on the HDR-FOX it is at /mnt/hd2/Tsr). The TSR buffer is used by the humaxtv process for live TV. This is not the same thing as the streaming buffer used (HDR-FOX) for iPlayer and YouTube, /mnt/hd3/Streamer_down_file (again I don't know where this is in HDR Mode on an HD-FOX, but the non-mod HD-FOX does not buffer iPlayer or YouTube). EP's experiment above proved the streaming buffer isn't used for Internet Radio, and the TV Portal apps each have their own code to support them. Supposing the TSR buffer was used, as far as live TV is concerned it appears to be encrypted.
There are no transport controls that might lead one to believe Internet Radio is buffered, and the low bandwidth of audio-only streams does not suggest any technical reason to need to buffer to disk (a small buffer in RAM would be enough). That does not rule it out, it just means that if there is a disk buffer nobody has found it yet.