The airline is about 54% owned by Temasek Holdings, which is the investment arm of the Ministry of Finance in Singapore. The airline however works independent of the government, and it is taxed accordingly as required by Singapore law.
There are no government subsidies in the workings of the airline, and the Singaporean government has stated more than once that it does not interfere in the running of the airline. One example I can think of now, is the recent AN-NZ-SQ saga. Apparently, SIA had asked the Singaporean government for help in communicating with the Aussie and Kiwi governments, but the government flatly refused to. It felt that SIA, as a publicly listed company, should be responsible for its own actions, and the government had no intention of asking the Aussie or Kiwi government for any help at all.
State money is NOT used by SIA to buy new planes. If you don't already know, SIA has one of the healthiest balance sheets in the entire aviaion industry, and has never announced a loss since its inception in 1972. The only other airline that can equal this feat is Southwest, and that airline is catering to a budget market, completely different from the market SIA targets. The airline has absolutely no need to ask for help from the Singapore government.
You are not being too hard on the airline. You have made a number of false assumptions, that simply because the airline is state owned, the government subsidises everything. You obviously have an extremely gross misunderstanding as to how Singapore and her companies work.