No, AIG was and is publicly held. Hank Greenberg was probably the largest shareholder at the time, but no individual owned more than 5%. The overwhelming majority of shares are held by mutual funds.
Years ago he did own a huge stack in AIG. In the 80’s. He has other Insurance holdings or had. I lived in Omaha for a bit and several friends who were well off knew him. No he did not own it when it bellied up.