I believe that I know the answer to the question regarding an "unattached" gymnast. My dd is a club and high school diver and the same thing happens during diving season.
During the high school season an athlete can not technically dive for 2 teams. When attending AAU or USA diving meets during highschool season, the athlete must list themselves as "unattached" and the points earned are not allowed to count towards the total club team score.
They can still attend meets with the club team and be coached by the club coach, but high school diving is considered the primary team during high school season. For girl divers, this is fall season, for boy divers it is winter.
So, I imagine there must be this rule regarding gymnasts!!