The work being done here falls into the category of "low background physics" --- they aren't trying to produce anything, and actually put quite a bit of effort into doing the opposite, by removing all sources of particles (e.g. sourcing materials free of radioactive contaminants, physically cleaning all surfaces and purifying all fluids involved, etc).

So the detector, if built properly, is fairly quiet, and you try to write as much data to disk as you can (e.g., if something even fairly-potentially interesting happens, you save it). Then when you analyze the data like this, you ignore the majority of what you've got --- only a teeny fraction makes it into an analysis of this caliber.

When doing this kind of thing, the analysts will plot the rate of events as a function of "distance from the outer surface" and confirm that it decreases, and in this case "is 0" inside of the detector used for analysis.

But keep in mind that all statements are made statistically, so it's not that the event _can't_ be an external neutron, but that it is _very_ unlikely to be.

In non-relativistic quantum mechanics, there is the concept of the "wavefunction," from which you can predict the results of measurements of a particle/system. But in most real-world scenarios, you can't actually compute the wavefunction, and so naively you can't make any predictions. But there is something called the "optical theorem," which relates a single evaluation of the wavefunction to a scattering cross-section, which is something that can be measured. If you're familiar with complex analysis, there is also the "residue theorem" which allows you relate individual function values with integrals of the function in the complex plane. Basically, you can combine those two relations to translate kind one integral (which you need to compute) into a different integral (which can be measured).

This is what was done here --- just instead of a simple QM wavefunction, the relevant concept is called a "vacuum polarization function."

The bottom line is that because axions would necessarily be very "light" (that is, very much not-massive), it is misleading to picture them as "particles" and better to picture them as "waves." So while it's true that axions would feel the electromagnetic field of an atom's nucleus, that's really just because it's an electromagnetic field. So to make an experiment which is sensitive by modern standards, you say "forget individual atoms, I'm just going to make a cavity and crank it up to large electromagnetic field." And that's exactly what is done in practice.

For example: axions, an alternative DM candidate mentioned in another comment, have seen a significant growth in attention in recent years, and the usual detector technology for axion searches is currently being refined and scaled up, from benchtop-scale, dedicated experiments to lab-scale, wide searches.

At the same time, different groups which have developed past WIMP detectors are merging to collaborate on the larger, next-generation detectors. And there is R&D and prototyping happening to create detectors which, although looking for WIMPs, are sensitive in entirely different mass ranges than those of yesteryear.

But, IMO, this is worthy of more study both theoretically and experimentally. An update to the evolution of the universe would be awesome!

Indeed, relevant to what an experiment like LZ might see, there really isn't much in the way of "predictions" which can be "contradicted." What we have at this point are mechanisms to calculate the interaction rate _given at least one free parameter_. If we were to detect a non-zero rate, then we would "know" the free parameter of a single-parameter theory underlying that calculation. If we were to continue to detect a non-zero rate, then we would try to do so using different materials, and look at the time dependence of the rate (or, really, the dependence of the rate on the Earth's direction of travel in our local galaxy). That would help us choose between different theories, pin down the free parameters, and confirm that what we're seeing is consistent with "heavy stuff just sitting out in the universe."

But, from a particle physics perspective, right now there are no predictions to contradict - just an opportunity to detect something.