So... ok, if the TARDIS came back before the ship exploded, that means she wasn't actually running away from the explosion. I mean, why would she, she's been in exploding ships before and she was fine.
So that means she was running from the edge of the universe. Except if that were the case, she wouldn't have been able to come back, because the edge of the universe is still there. So she must have been running from the Not-Things.
Because, as established, it takes time for the Not-Things to learn how to copy things. They need to study you, read you, before they can become you. The TARDIS coming back at the eleventh hour meant they didn't have that opportunity.
This does mean that without the HADS, there would have been a Not-TARDIS, and I think that would be the actual scariest monster in all of Doctor Who.