Airplane actually belongs to S. Brinn, L. Page and E. Schmidt. Brin and Page are the founders while Schmidt is the former CEO of Google. Former Qantas 767ER. Also own a B757 and several Gulfstream V/550' with a 650 on the way. As someone else mentioned it hides under he banner of BCH.
It was in Fiji to hook up with one of the owners yachts.
With the exception of a G550 that came to Google through the Motorola buy-out, Google does not own any aircraft.