ISTR that the opening titles (or opening sequence?) were split on BBC Four and BBC World (don't think it had rebranded to be World News by then?) with one of the presentation areas playing in the 'other' one, and joining the programme on a post-titles wide shot?
I may be misremembering.
I'm pretty sure you're correct. This was certainly several years before the BBC World News rebrand.
The change to the green set and dropping the 'BBC Four News' name happened at the start of 2004, and the change to 'World News Today' happened in 2007.