But in your example, it is explicitly not considered and rejected:
From the "considered and rejected" point of view, you are not an atheist. From the privative view, you are. From the point of view of many, if not most, christian churches, you are an atheist (or perhaps a heathen, or even a savage).
So...as you say, "[t]here would have to be, if it is considered and rejected." But there need not be a clear black-or-white split if we are speaking of atheism in the privative sense. You might believe, based on your criteria, that a 5-yr-old is able to make such a decision; if the child has not yet decided by that age, he or she is a privative atheist. I might believe that a 10-yr-old (or 14, or 3, or whatever) is old enough; if my cutoff is different from yours, because my criteria are different, such is the nature of operational definitions, and as long as we make our criteria known we can be comfortable disagreeing.