It says what it says (Parent or Legal Guardian). So here's the definition of "Legal Guardian" (since we can exclude your cousin as being a Parent):
A Legal Guardian can:
1. Sign for medical care of a minor
2. Assume parental roles such as;
a) Custodial care and nurture.
b) Provide for the life, welfare and benefit of a minor.
3. Enter into legally binding contracts on behalf of a minor.
4. Assume legal responsibility for said minor.
The above is an abreviation of the legal requirements placed on guardians of minor children.
The purpose for this requirement in AA is that legally, minors cannot make legal decisions for themselves. Adults are accorded that responsibility. So, if you injure yourself at an AA event, you may not want to sue AA, but your parents may. And in fact they would have a legal "right" to sue. However, if your parent or legal guardian are with you at an event, the eyes of the law speak "implied consent" because they saw what you were doing, and did not stop you from doing it.
I hope this answers your question.
TheRev