Not sure what Zoll means to "chase" it, assuming that the "it" is "soreness". I will guess that chase means to try rest first, and if that's not the answer then they would start the more aggressive treatments like anti-inflammatories, with a notion of playing catchup at that point.
He goes on to describe their course of action as playing it safe, and maybe that's the medical opinion of 99% of qualified doctors, I wouldn't know. I probably would have reversed the terminology and called "rest" the play-it-safe option.
Not word salad, exactly, but his quote took more than a little parsing on my part, and I'm still left uncertain.