TL;DR: They compared the metallurgy of two different samples, which IMHO totally invalidates the result.
The setup revolves primarily around "Johnson-Matthey purifiers", which are made by a manufacturer for industrial hydrogen gas purification. It isn't designed to have calibrated or consistent metallurgy for this kind of scientific experiment.
They're essentially a long Pd-Ag tube sealed in a stainless steel pressure vessel and also the tubes have supporting stainless steel springs inside them.
The experimenters had only two(!) of these filters, both sealed in the factory. They had to cut them open to access the Pd-Ag tubes inside for analysis.
A) This is a destructive test, so they had no way to run the experiment on one tube for longer and longer periods to demonstrate a steady increase in the contaminants.
B) They didn't take a control measurement of either tube before commencing the experiment.
c) They have no reason to assume that the metal purity of the tubes is anywhere near consistent enough to compare two different tubes, which are likely to have been manufactured on different dates from different metal sources and hence would not be consistent enough for this kind of experiment.
D) Individual tubes could also have had point-to-point variations, which they claim is the result, not the error! That's insane.
E) This is a long-running experiment (months) with many actions taken on the filters. Connections and disconnections of gas sources, high temperature cycling, flushing with various gases, etc... It's entirely conceivable that a contaminant got into the tubes.
Essentially, the only scientific way to run an experiment like this is to manufacture a tube yourself, using either very high purity metals or a very well characterised and homogeneous alloy. Then you'd have to take samples at multiple points along the tube and at several different times during the experiment. You'd also want to make sure that the entire experiment is housed in a metal that is similarly well characterised. At least a dozen such setups would need to be run in parallel, using the exact same setup except for gases used.
They did none of this. They simply noticed a filter got hot, cut it open, and assumed that what they measured was an increase relative to a different unused filter they had lying around.
This is garbage science.