Reversing the paradox

Okay, it's a long time since I've watched Last of the Time Lords (will try and have a look tonight) but I just got thinking: when they reversed the paradox, everything on the earth got reversed but the Valiant didn't, right? So what happened to those people who were on the Valiant right before the paradox kicked in - all the film crews and world leaders or whoever they were? I know the President got zapped and so there wasn't a body (right?), but there were other people present at that point who didn't suddenly appear on the bridge of the Valiant when time was reversed.

So where did they go?

And no, I'm not expecting an actual canon explanation for this, because they don't think things through that thoroughly, but can anyone suggest something that makes sense? At the moment, all I can imagine is them somehow popping up at their homes or something, going "Whu....?"