No atheist with any sense will claim that the negative has been proven and a god cannot possibly exist. You're trying to define atheism out of existence, but all that does is removes a useful label. The two positions I set out above are both common, so it's useful in discourse to have two separate terms for them. Widening one term so as to include both, while narrowing the other term such that it fits almost nobody, is not helpful to the discussion; nor does it undermine either of the two positions.