Except atoms aren't atomic: they can be further subdivided. In the original sense of the word, we still don't know whether there are atoms.
> It means we have a statement for which we can generate additional evidence at will. No matter what your threshold for evidence needed is, it can be met.
Reading the same book over and over again only gives you evidence about what the book says, not whether the words in the book are true. Likewise, performing an experiment over and over again only gives you evidence about what the experiment does, not any models that generalise its results (beyond the marginal, diminishing-returns "we're pretty sure this experiment's results match up").
Nothing is ever beyond doubt; only beyond reasonable doubt.