For Parkesquay:
All DVDRs will accept an RF In signal and provide an auto-tune facility to properly receive this signal. The tuner converts the RF signal to AV format which is passed to the recording section. (Other signals entering the DVDR, either via AV lead or a Scart lead, are already in AV format). When the disc is played back, the signal is once again in AV format. The usual way to pass this forward to the next device in the chain (in this case the TV) is to simply keep the signal in AV format and pass it through either a Scart or AV lead.
If the signal has to passed to the TV via its aerial socket, the DVDR will have to include an RF modulator (which adds to the cost of the product) to convert AV to RF. This then goes along a fly-lead to the TV's aerial socket, where the TV's tuner circuit once again converts the signal back to AV. (This two-stage conversion also degrades the signal). So, in most cases, the manufacturers of DVDRs (and other devices, like Freeview boxes) don't bother providing an RF modulator because this would increase the sale price of the recorder and because most TVs have got Scart sockets
anyway.
You correctly observe that most (probably all) DVDRs have got an RF Out socket but this does not receive a signal from the DVD through a modulator. In most cases, the RF Out socket is connected directly to the RF In socket. (i.e. all that comes out of the 'Out' socket is the same aerial signal which was fed into the recorder). This permits the owner of the TV to receive a direct RF signal (just as if the aerial was plugged directly into the TV) but it doesn't let them receive the signal from the DVD unless they also use a Scart lead (which, in Brownlow's case, is impossible).
Chris