Does this mean that adults are allowed to do all of the design, construction, coding, analysis, and documentation for the robot? In other words, is it conceivable that a team could be comprised of a group of adults that have created the robot and a group of students that are there only to drive the robot at tournaments?
The VEX Robotics Competition leaves it up to teams to decide how they operate. There are no specific rules about adult involvement on a team, outside of what is stated in the thread you linked to in your question. Any sort of rules about adult involvement in the above described phases of the engineering design process would be completely unenforceable. As such, the extremely unrealistic situation you described with students having zero involvement with the robot would be legal.
We want students to seek out the expertise of adult mentors to enrich and enhance their learning experience as part of the VRC. We hope that all adult mentors will carefully evaluate their involvement on a given team and make sure the degree of involvement does not become so large that it actually detracts from the overall experience of the students. What this exact level may be is highly dependent on the students involved; we leave it up to the adult mentors to work with the students to determine the precise balance.