Genetics absolutely has something to do with it. If a non-native Australian came along and started self-identifying as an aboriginal they'd be lambasted, and excluded from this advisory body as it's not meant for them.

States and nationalities =/= ethnicities. Someone can be an American by being a citizen of that country, past or present. Someone can be Californian by being a resident of that state, past or present. Someone is Aboriginal Australian by virtue of being born to another Aboriginal Australian. Nation states and ethnic identities are utterly different concepts. When I fill in a government form, I am a UK citizen, and identify as a British person; not as any of the other multiple options available to me. There are two separate boxes. I can become a US citizen, or a Canadian citizen, or a Mexican citizen, and identify with that nationality. I can't decide one day to become an Arab or Gypsy ethnicity, even if I lived on the Arabian peninsula or replaced my car with a horse and trap.