Bohm,
I agree with your reasoning in general, but you also can agree with me, that science also operates with probabilities. For example, Einstein's general relativity theory has worked well so far for science, and has allowed scientists to perform spectacular feats, but there are phenomena in the universe that the general relativity theory is unable to explain accurately, especially when it comes to extremely small particles, or extremely large portions of the physical universe. However, because the general relativity theory works in most cases, it is widely accepted and is used to explain how the physical universe works, even to predict speculatively certain phenomena that haven't been observed yet, or others that, having been observed, don't seem to fit the theoretical model entirely but can be partially explained by it. This is why scientists are open to the possibility that there are other explanations to the way the universe works, namely, the holy grail of fusing the general relativity theory with quantum mechanics.
The same sort of extrapolation is required when atheists discuss the existence of deity. They have a skeptical model that has worked this far - because no deity of the sort of the bible deity has been sufficiently validated by evidence so far - but it's merely a logical extrapolation that "no deities exist". That model has worked so far, and I may agree that it might continue to work. But I think that it's a more sound reasoning to prudently claim that "god is absent", because it leaves room [albeit a very remote probability] that a deity may exist somewhere within the universe that we haven't been able to observe yet. Because we have been always operating under the assumption that a deity has to interact with humans. What if it doesn't? What if a deity has started life and then left it to develop on its own? What if a deity doesn't require worship? What if a deity doesn't care a bit if we live or die? Sure, all of this is speculative, and by now you should know that I'm not apologetic of theism. But I find a huge logical flaw in the modern atheistic claim that "no deities exist" because it negates the very rational thinking that science is based on.
Also, please note that I agree with you when you say:
The problem is that how easy it is to confirm (or rule out) the existence of X should not affect our belief if X exists.
This is true. Still, as you point out, it's a matter of belief. The theist claim that God(s) exist, and the atheist claim that "no deities exist" are both a matter of belief. None of these propositions is soundly rooted on evidence. The first is based on false evidence, and the latter is based of the lack of evidence.
Eden