Here are a couple of specifics from my experience as a coach:
If an athlete’s parent hires a private coach for their kid, and the parent asks you if the private coach can be at the next high school meet and talk to the athlete, cooperating with the parent would mean letting the private coach help.
If an athlete’s parent shows up to help officiate the morning (JV) portion of an all day meet and says he is requiring his son (the star athlete) to work with him all morning as punishment for staying out late, cooperating with the parent would mean allowing him to do so, even though the athlete was scheduled to compete in the invitational section that evening.
Parents naturally believe that, in times of disagreement, they know better than the coach what is in their child’s best interests. I think that “cooperating with parents” means that you will allow them to have at least some input into your decision making process when those conflicts arise.