If I understand you correctly, then I agree. However, to me it seems clear that human beings discount probabilities that seem to them to be very small, and it also seems to me that we must do that, because calculating them out and having them weigh our actions by tiny amounts is impossible.

The question of where we should try to set the cut-off point is a more difficult one. It is usually too high, I think. But if, after actual consideration, it seems that something is actually extremely unlikely (as in, somewhere along the lines of 10^{-18} or whatever), then we treat it as if it is outright false, regardless of whether we say it is false or say that it is simply very unlikely.

And to me, this does not seem to be a problem so long as, when new evidence comes up, we still update, and then start considering the possibilities that now seem sufficiently probable.

Of course, there is a danger in that it is difficult for a successive series of small new pieces of evidence pointing towards a certain, previously very unlikely conclusion to overcome our resistance to considering very unlikely conclusions. This is precisely because I don't believe we can actually use numbers to update all the possibilities, which are basically infinite in number. It is hard for me to imagine a slow, successive series of tiny nuggets of evidence that would slowly convince me that Zeus actually exists. I could read several thousand different myths about Zeus, and it still wouldn't convince me. Something large enough for a single major push to the probability to force me to consider it more thoroughly, priviledge that hypothesis in the hypothesis-space, seems to be the much more likely way - say, Zeus speaking to me and showing off some of his powers. This is admittedly a weakness, but at least it is an admitted weakness, and I haven't found a way to circumvent it yet but I can at least try to mitigate it by consciously paying more attention than I intuitively would to small but not infinitesimal probabilities.

Anyway, back to the earlier point: What I'm saying is that whether you say "X is untrue" or "X is extremely unlikely", when considering the evidence you have for and against X, it is very possible that what happens in your brain when thinking about X is the same thing. The hypothetical skeptic who does not know to use the terminology of probabilities and likelihoods will simply call things he finds extremely unlikely 'untrue'. And then, when a person who is unused to this sort of terminology hears the words 'X is very unlikely' he considers that to mean 'X is not unlikely enough to be considered untrue, but it is still quite unlikely, which means X is quite possible, even if it is not the likeliest of possibilities'. And here a misunderstanding happens, because I meant to say that X is so unlikely that it is not worth considering, but he takes it as me saying X is unlikely, but not unlikely enough not to be worth considering.

Of course, there are also people who actually believe in something being true or untrue, meaning their probability estimate could not possibly be altered by any evidence. But in the case of most beliefs, and most people, I think that when they say 'true' or 'false', they mean 'extremely likely' or 'extremely unlikely'.