When I say, "I don't believe in god," I say it in the same vein as, "I don't believe in Bigfoot," or, "I don't believe in fairies." I don't mean that they might exist; rather, I don't allow for their existence at all. That's strong and implicit, and where the topic is god, it's strong and implicit atheism. It expresses my belief, my opinion, with no ambiguity.
The person who, by whatever logic, may allow the possibility that these things exist, doesn't fit that idea.
Edit: Explicit, not implicit. Sorry, I should have proof read better, but I'm busy offline.