I place mechanistic theory prior to statistics in science. Mechanistic theory can be tested, statistics are a kind of test.
If a statistically-insignificant result shows consistent, though non-significant deviations, such as the kind seen in Figure 11, then it tells me it's worth investigating whether mechanism(s) are explaining a very small portion of the variation that will not, in itself, show up as statistically significant, as it's being swamped by variation in other parameters.
You can extract surprisingly small signals relative to variation in other parameters. But if it's actually swamped, then it might not be real, so go get more data.
So basically you're telling me that if I can visually see a consistency that does not show up in their statistical test, then they aren't running an appropriate statistical test on what I'm seeing.
> But if it's actually swamped, then it might not be real, so go get more data.
Even better to design other experiments.
Either they're not doing the right statistics, or it's a "consistency" that is much more likely to show up randomly than you naively expect, and the study needs to be repeated or enhanced.
Sometimes you can see a pattern that's just a figment of chance. See also: numerology, jelly bean xkcd