Jetstar Asia is 51% owned by a Singaporean businessman (a Qantas proxy) and 49% owned by Qantas. For all purposes and intents, it is an Australian airline using a Singapore AOC to operate. Obviously Singapore's civil aviation authority realises this and accepts it. It was Temasek Holdings that sold its stake in Jetstar Asia to the Singaporean businessman anyway, so the Singapore establishment at large accepts this.
Jetstar Asia has already been competing with SIA for rights given to Singapore carriers. As a Singapore carrier, Jetstar Asia can use Singapore's very liberal rights to Europe, including operating unlimited frequencies to Stansted or Luton or Gatwick or Manchester if they so wished. Jetstar Asia's CEO said they're looking at operating medium to longhaul services from 2011 using A330s.
The average man in the street in Singapore probably doesn't care who owns Jetstar Asia, and will be pleased with the cheap fares that competition brings.
Qantas through Jetstar Asia has far more to gain from Singapore than SIA through Tiger Australia. Qantas through Jetstar Asia gets all of Singapore's rights to the EU (nearly open skies except France and Germany), soon-to-be ASEAN open skies, and nearly unlimited third and fourth freedom rights to China. That's India, China, South East Asia and the EU - more than half the world's population.
SIA through Tiger Australia gets...... 21 million people spread across a vast land mass.
Go figure who got the better deal!