One of the interesting things about the negative proof fallacy, is that it seems to assume a binary state of affairs. That is, statements are either true or false. So if you can't prove that something is false, it is true, the fallacy runs.
But of course, this is not correct. Many things can be said to be true, false or uncertain or unknown. Thus if an atheist can't prove that there is no God, this does't mean that there is, but that it's uncertain, (although the atheist may argue that it's implausible or contradictory).
But this non-binary state also seems to apply to incredulity. For example, someone says, 'I can't see how the brain can produce consciousness', and then goes on to say, therefore God does it.
But again, the middle term is missing, the cause of consciousness is uncertain or unknown. This doesn't mean that the brain does not produce it! That's why neuroscientists are working on it.
Another one that pops us - you can't say what happened before the Big Bang, therefore God. Well, no, it's unknown.
So some theists seem to use black and white thinking a lot; hence, the (mis)statement, you can't prove there is no God, therefore there is.