The article never clearly describes the brute-force approach. Is it just a matter of looking for statistical outliers along all the different dimensions they can think of? How would they then distinguish the "interesting" outliers from random flukes?
The gist is that you would roughly look for deviations from theory on one (probably small) dataset, you'd identify any regions of interest and then run a proper analysis of that region on a different dataset to see if the effect is real.
The problem with this approach that I see is that it's much more likely to pick up lingering detector issues than the regular test-a-theory. (The difference between looking for a specific thing in a specific place vs picking up anything unexpected.) I wouldn't worry do much about purely statistical artifacts because those can often be worked out with prescriptions and remeasuring. The systematic but not-understood biases are the ones that should plague this approach since in the extreme they would need an independent experiment. I wonder whether CMS and Atlas are sufficient for that.