[Eugenia Gabrielov]

The college admission process is a strange one - you practically sell yourself, searching for a balance between too involved and not involved enough, for an even ground of leadership, participation, and genuine personal interest in an activity.

No, it is not right that the student has exaggerated their participation. If they are asking for a letter of recommendation from the lead team mentor, it is very possible they will be called on it. Other than that, the only thing that can really solve the situation is changing the way you handle team participation. Good luck!