Science can handle the possibility that correlations are false. If the correlation between drownings and phenomenon x becomes apparent, the next step is to formulate a new hypothesis that can be falsified and continue testing.
For example: more people swim in the summer. Also more ice cream trucks rolling around in the summer. Let's see if "it being summer" (or something else) doesn't better explain the supposed correlation.
If poly is taking up the mantle of Humean skepticism, then I think your criticisms are apt. But I don't think these criticisms are good criticisms of science in general. If only one experiment could be done ever, then yes... a false correlation is devastating to gnosis. But science can take hundreds of cracks at a problem. So one bad result doesn't seem like an issue to me.