In this case it is largely empirical fact. There are cosmic rays hitting the atmosphere every day that are 10^21 electron volts, as compared to 10^12 for the particles in the LHC. From these incredibly high energy collisions there are huge cascades of particles as the cosmic ray interacts with the atmosphere. These are *seen* not theorized. In these cascades the energy gets split among all the particles affected and the particles they decay into. In this "shower" are a large number of interactions just like those that occur at the LHC. This is fact not theory. The basic point of article is that given this known fact, and the assumption that these black holes *are* made in such interactions, what do we expect the danger to be given the fact that certain astronomical objects are not obviously adversely affected by this process.
The main theoretical uncertainties come in is in the energy scale at which these black holes are created in such collisions, but the authors argue that we can place a conservative bound on the effect simply by comparison with these more dense objects.