Isn't denial a positive belief system? I am not even saying that you deny God. I am saying that you deny that you know there is no God.
I know there is an Eiffel Tower, but that does not change my belief system. I know there is an Atlantic Ocean, but that does not change my belief system. I know there is no spaghetti monster, but that does not change my belief system. I know that there are no people who think my belief system is stupid. That does not change my belief system.
Believing something that is not true, does not change the fact that it is not true, nor does it make it true, it just means they have decided to think a lie is true.
That is why belief is not in the equation. If an atheist is an atheist because he "believes" he is, then that is not based on knowledge, but on their personal cognisance. He may try to deny my personal cognisance, but it is futile. Knowledge is a funny thing when it cannot be revealed to every one. There are humans who have never seen an airplane. How would you convince them, without showing them one? Does their lack of knowledge make them non-human?
It is plain that they know there is no God. It is plain that some humans know there are no airplanes. It is not that there are no airplanes. It is the fact that the concept is foreign to them. Yes a bird can fly, but humans cannot.
So why is a belief system, which is subjective, be used to define knowledge that is objective?
Even if "that knowledge" is a foreign concept to many?
Evolution is a foreign concept to me and that fact may have been shaped by my belief system. But what if it was not shaped by my belief system? What if inteligent people on the other side of the world with a totally different belief system came to the same conclusion?
Remember that a theist does not truly know, unless that knowledge was given. There was no refutal of that "fact". As a human the concept of God is to me just as foreign as landing on the moon. While my belief system thinks that we did both, and an atheist will only agree on the moon landing. I saw the news flashes about the landing, but my concept of God was even stronger at that point in my life. Now that is a subjective anectdote, but the principle is the same. Why did God leave a more objective thought in my head than the moon landings did? I was 2 years old!
Knowing a lie is a lot harder to explain than knowing a truth?