Talking Business on Saturday evening appeared to be a 720p upscale to 1080i, complete with black bars which wasn't the case when broadcast on BBC World News.
Do you mean 720p? 720p is 1280x720 and is the same aspect ratio (and for a lot of content effectively quite difficult to tell apart from) 1920x1080.
There should be no black bars anywhere if it is a straight upscale - as they are the same ratio. If there are black bars top and bottom and different width black bars left and right then that suggests (assuming the display isn't differentially cropping) that something has gone awry. Unless you are looking very carefully on very demanding material 1080i25 and 720p50 (aka 1080/50i and 720/50p) are pretty similar in quality terms - particularly on talking heads at BBC News bitrates...
You'd possibly see black bars left and right with poorly handled SD (where 720x576 has been scaled to 1920x1080 rather than 702x576 - which is the actual 16:9 active picture area in SD - with black bars padding either side).
One area where things can go wrong is that 1920x1080 isn't actually recorded in most digital systems in that format (as it isn't a nice MPEG multiple). Instead 1920x1088 is recorded, with 8 lines padded with black on recording and cropped on replay. That can sometimes cause very small amounts of scaling errors if it is handled incorrectly.
However it sounds as if something worse has happened in this case - and I think I've seen something like this happen before. Could be that the show has been delivered in an odd ball format - particularly if it was edited off-site in the field...
** EDIT - just seen the screen grab. That looks like a poorly handled 576i SD up convert, possibly from a down convert with the downconverter probably doing the right 1920x1080 to 702x576 with a 9 sample black pad each side to generate 720x576 (which won't be seen on an SD set as that should only show the 702x576 portion), but then the 720x576 (not the 702x576) portion scaled back up to 1920x1080 - giving you black bars each side in the 1920x1080 frame.
So many people think you should show the full 720x576 frame - you shouldn't...