Their point is exactly that the trigger systems are controlled by algorithms based on current theories, which so far have shown nothing for all their efforts.
I haven't been in the field since the LHC started operating but from memory it was exactly billions of events per second and storage could only keep up with hundreds.
No one is setting these things up to go "hmm a particle on a totally unusual trajectory - but not where the Higgs should be so junk it".
If by "so far have shown nothing for all their effort" you mean that no new results were found, that isn't due to the current theories being bad: in fact, it is due to them being too good: they describe the results too well and thus there is not enough difference between the current theories and current results that would require a new theory.
(turned out they did, but nobody at the time knew to account for perturbations caused by the as-yet-undiscovered Neptune)
And depending on how far you want to take this, the neutrino probably would've been dismissed, too, before eventually being detected.
"Oh look, Uranus is doing that odd things again. Doesn't fit in with Newtonian mechanics or my current pet theory so better throw it out."
> From a billion events, this “trigger mechanism” keeps only one hundred to two hundred selected ones. … That CERN has spent the last ten years deleting data that hold the key to new fundamental physics is what I would call the nightmare scenario.
These words show their opinions come from someone that does not know/understand the technology behind these systems and behind the computing power and capabilities at CERN. Of course, they have limitations, but are the kind of limitation that keeps pushing technology forwards. Using quotes on the trigger mechanism is saying how strange those concepts are for them.
The trigger system is a fine tuned filter that allows the electronics to work, otherwise they will be overloaded and will crash as they will be receiving a rate of data that simply can not be handled. How this trigger is being set depends on the specific physical process that is being studied and is supported by theory and simulation, the scope that can be tested is also limited so the selection is highly scrutinized and reviewed