First of all, the feature to download catchup has been on BuzzTV app for ages now. I use it all the time.
First of all, what you are asking is NOT related to buzz really, since you are talking about a 3rd party app. The issue is imPlayer and the way it has implemented it.
But just a summary, you will NOT be able to "move" the file, since you probably don't have write permission on that directory, .In order to move you technically copy from a directory (Which only needs read permission from that directory), but you need write permission in destination (which I assume you do if you are copying to a USB stick or something else). But to complete the move, it then deletes the file from that directory, which requires "write" permission which you do not have. OK, I over simplified it, since filesystem is a little different on android/linux than windows (mostly a quick inode update for a move on android), but permissions all still need to be there., and that is the general sequence of events.
Since the buzz boxes are not "rooted" you don't have any way to gain write access to that directory.