The thing I don't get is that this means they have time travel technology, too. So why are they fighting the Doctor in such a bizarre way, when they can just travel to any point in time in which they know the Doctor will have been and eliminate him then and there?
And since the Doctor is always fluttering through time, they likely know where he's going to be in his future, too. So any argument about not being able to do it because of some great impact on the timeline means they can't kill them at all if they know he continues to be successful long into his relative future. Which, clearly, is not a concern for them, so there's no reason they can't take him out in his past, either.