Yes, it's true that you have to download it via BBC's iPlayer but you can only keep it on your computer for a certain period of time (maybe as little as one week or upto three months). It depends on the programme and is down to UK Copyright Law and the BBC's own internal rules. Even though you've downloaded it, if you don't view it within the time limit, it will 'expire' and get removed from your computer automatically.
You can record it instead easily using software to 'grab' the video as its played. See site resources for a link with a 'how to' on recording iplayer.