As an experimental scientist, I can, with certainty, state that you are wrong when you claim "science is about provability."
It is extraordinarily difficult to prove something experimentally. Most advances come about because we (both individually as experimentors, and collectively as members of a given scientific field), think we've accounted for most potential confounds and artifacts, not because we've conducted perfect experiments. Biological sciences, especially, suffer from a huge number of uncontrolled variables that often we are not aware of, but impinge mightily upon our results. Biology, to continue, is noisy. Very, very noisy. In my lab, we measure phenomena related to visual perception, and I can tell you unequivocally that individual variation usually swamps any underlying phenomenon we examine (meaning, we need to measure with lots and lots of individuals to make sure we aren't being fooled, and even then, we can easily get fooled).
Rarely, if ever, do we prove something experimentally. It's only through the consensus of reproducibility that scientific facts get established.
Piltdown Man, to discuss your example, was due to observational error (ie, a hoax), not experimental evidence demonstrating provability. Observational science, as opposed to experimental science, is rife with missteps and re-interpretations. Look up the history of shooting stars, as one example -- they were considered purely terrestrial phenomena well after the establishment of the United States as a country. It took repeated observational events, not experiments, to establish that meteors are astronomical in origin.
Reproducibility is the cornerstone of modern science. Everything else is consensus. We think we know things, and mostly, we've been correct with a high degree of probability, since we've been able to take given conclusions and build, predictably, upon them. But, every now and then, even firmly-held beliefs with eons of structural experimental integrity are demonstrated to have been mistaken. There is very little scientific truth, merely scientific certainty. If you want absolute truth, look to mathematics instead.