So when anybody says "we showed X was critical", they actually mean "we plotted a fuzzy cloud of data points on a log-log plot and fitted a line through it", nothing more. But you can fit a line through anything. Even a normal distribution shows up as a line on a log-log plot if your data has a small enough range.

Criticality studies trade on the reputation of physics, where the idea came from, and there it works fantastically. For instance, we can measure critical exponents for liquid/gas phase transitions to three or four significant figures, and even predict those numbers from pure theory. Applications outside of physics usually have barely one significant figure, if they're even measuring power laws at all, and no predictive theory.