You are placing two kinds of acceptance; acceptance that something "might be true", which is acceptance of the possibility (which, I would argue, most atheists still take part in, as they don't claim that God is an impossibility, but merely hasn't been supported nearly enough), and acceptance that something "is true", which is "belief" as it is used to describe "theism" and "atheism". Now, if one "accepts that God exists", they believe. If they merely "accept the possibility that God exists", they aren't expressing any beliefs that would have any bearing on theism or atheism. Thus, I feel that you are comparing apples and oranges. If you are going to apply logic, logic would dictate that you confine your scenario to "belief in the existence of God" rather than any mention of "belief in the possibility that God might exist". The former is "theism", the latter is something completely different.