> They claimed the paper shows how radiometric dating is unreliable, because radioisotopes can be leeched or absorbed which would through off the ratio of daughter to parent isotope.

An important aspect here is that not only are these considering relatively rare areas (i.e., areas influenced by radioactive testing and/or natural reactors like Oklo), they are (1) mostly tracing radionuclides that are not used in radiometric dating and (2) more importantly considering migration into and out of material (i.e., minerals) that are not typically used for radiometric dating. That radionuclides are soluble and thus easily mobilized out of oxides like what this paper focuses on is precisely a reason why many of these minerals are not considered suitable for geochronology. Minerals that we actually use regularly for geochronology (e.g., zircon, monazite, apatite, etc.) are used in part because they tend to be relatively resistant to these kind of effects.

Additionally, the underlying premise seems to be that geochronologists just uniformly accept the assumptions of closed-system behavior when in fact we routinely consider, and test for, open-system behavior as a matter of course in most analyses (e.g., Schoene et al., 2013). The degree to which we are concerned about open-system behavior, and potential remedies or corrections, depend on the method. We generally expect that U-Pb dating in zircon will reflect closed-system behavior, but still almost always check via measuring both ^(238)U-^(206)Pb and ^(235)U-^(207)Pb ages whereas we expect the possibility of open-system behavior of something like ^(234)U-^(230)Th dating in carbonates is relatively high and do a variety of things to check whether dates are valid or influenced significantly by open-system behavior.