When presented with a perpetual motion device, I can have faith that it will not work. Thanks to the Second Law of Thermodynamics, my Bayesian confidence in that belief is quite high, so it is not as if my faith is stepping out on a limb. But I have not proved that the perpetual motion machine won't work by actually examining it and finding the flaw, I simply have very-well-founded faith that such a flaw exists. Faith is a perfectly appropriate word here.
(I parenthesized "effectively" up there to avoid a massive and irrelevant discussion of exactly what 100% means, though it still pokes through. But is interesting to note that since reaching 100% confidence is very difficult, "faith" comes up in virtually every decision you make.)
As an aside, if you're going to be talking about Bayesian probability, you should know better than to call "100%" confidence just "very difficult"...
Oh, and part of my point is that common usage is wrong, on the grounds that the "common usage" is incoherent, meaningless, and information-free. (I basically take it as axiomatic that the worth of the definition of a word can be measured along those axes; I'm generally a descriptive grammarian but that doesn't mean I have to throw all standards out.) Use something more like my definition and you get meaning again.
Of course it's illuminating to analyze the question and figure out where, exactly it's gone wrong, much like it's fun to puzzle out subtly flawed mathematical proofs that 0 = 1.
But in the end an argument that concludes with something equivalent to "therefore, causality is broken" or "therefore, time is meaningless" doesn't really warrant serious consideration unless it's backed by some very serious evidence.