... people with high justice sensitivity showed more activity than average participants in parts of the brain associated with higher-order cognition.
What is the activity being measured relative to? One of the issues with any brain imaging study is the baseline condition you make comparisons with. To state that you saw more activity is only meaningful if you believe the baseline was appropriate.
Brain areas commonly linked with emotional processing were not affected.
Again, this must be relative to the baseline chosen, which the story doesn't mention but relies on. For example, in this study they do a comparison of Good vs Bad and then do the reverse comparison of Bad vs Good. If the emotional parts of the brain are equally active for both those conditions, then they'll simply disappear in the contrast. You may or may not care about this depending on your research question, but it does affect the claims you can later make. To be clear, I'm fine with the paragraph so far.
Individuals who are sensitive to justice and fairness do not seem to be emotionally driven. Rather, they are cognitively driven.
This is where I take umbrage. Nothing in the previous para claimed (or demonstrated) that there was a fundamental distinction between cognition and emotion per se. Yet this quote tries to boil it down and makes claims about the emotional aspects that the study cannot support. That the emotional regions of the brain showed no difference may simply be an artefact of the study design. Having read the paper, they didn't have a proper baseline comparison so I treat any claims related to emotional processing with suspicion.