Specie A (with this disease) stop cannibalizing after seeing the outcome, better chance of survival.
Specie B (without this disease) eat themselves to the last person... Lower chance of survival as a specie.
Nature "cares" by generating lots of options, then let the fittest to survive. So while nature doesn't intend or plan for a specie to survive, the outcome is no different from if it did. I believe the OP means "care" in this sense.
Personification of "nature" is a shorthand. No one actually thinks "nature" is an intelligent entity making independent decisions about the biology of creatures (when people refer to that, they call it "God").
Rather, they mean "Could this be the way that the species' internal biological and evolutionary processes are involved in preventing cannibalism?" Personally, I think "nature's way" is a highly preferable and convenient shorthand. :)
I wasn't objecting to the teleological language (as you say, it's a convenient shorthand for an unconscious process). Rather, the idea that "species survival" is a relevant variable for selection to target is thoroughly confused (or, nature cares deeply for the gene, but knows not of your "species").