Why would life depend on the low concentration that is not even toxic to all of the life here on Earth?
It wouldn't, and the study isn't saying that it would.
The point is about narrowing the search space. An analogy would be guessing passwords. If I want to guess the passwords of the people I work with I can start with the assumption that it could be anything, which doesn't narrow the space and makes the task impossible, or I can start with the assumption that it'll be based on a dictionary word with some numbers because all my passwords are like that. I'll definitely miss some passwords that don't fit my assumption but I'm far more likely to get some positive results (assuming my way of generating a password is common in the universe.)
Fair enough, but it would be counter-productive to have too restrictive a filter.
Take the CO criterion, for example. While it is reasonable to point out that CO may be present in high concentrations in many planetary atmospheres, at levels that would be toxic to life evolved on earth, one must consider that life might evolve in a way that tolerates or even exploits it. Oddly, the authors acknowledge this, yet, apparently without any counter-argument, still include CO as a probable show-stopper.
As the way to search for life beyond the solar system is to look at atmospheric composition, an alternative way to look at the 'CO problem' is to say that an abnormally low CO level on these planets might be a hint of life.
It wouldn't, and the study isn't saying that it would.
The point is about narrowing the search space. An analogy would be guessing passwords. If I want to guess the passwords of the people I work with I can start with the assumption that it could be anything, which doesn't narrow the space and makes the task impossible, or I can start with the assumption that it'll be based on a dictionary word with some numbers because all my passwords are like that. I'll definitely miss some passwords that don't fit my assumption but I'm far more likely to get some positive results (assuming my way of generating a password is common in the universe.)