Presumably few of the Tiger passengers stranded in Bali knew (or cared) that they were flying on a Virgin plane with a Tiger paint job. Or that Tiger had no Air Operators Certificate for the route.
Suppose the situation was reversed. Would Australia allow Lion to fly here without an AOC, using planes leased from Garuda?
Likewise how many passengers flying on Cobham think they are on Qantas; just because Cobham paints its Boeing 717 jets with a Qantas logo?