And yet it doesn't. Because if any type of theist says something along lines of, "I equate God / deity / divinity with this concept," then some atheists won't simply stick to, "I am without a belief that this is God" but will pretty much venture into territory of, "you can't say that. That's not proven. We have proven that concept to mean something else than how you are using it. You need more proof." As if all of that is on the theist, when as I've explained numerous times, atheists actually have beliefs of what would constitute evidence (for them) and this varies from atheist to atheist. Thus the ambiguity.
Once evidence is allowed into the picture via strong atheistic position attempting to dictate how the discussion must look, it exposes the atheist position to a plausible string of definitions that will first be placed on theists. But with theist who's not asleep at the wheel, it will become the two way discussion in needs to be, for clearly many atheists aren't actually lacking a belief, they are outright rejecting it. To varying degrees, which are worthy of being defined for sake of argument.