So many minor partners to keep track of, and so many complications/exceptions! I have a feeling that part of the benefit of low cost carriers splitting off from the parent is that they do not have to pay the lounge access fee to partners.
I have been denied from Air China lounge when flying one of their multitude of domestic partners (Shenzhen/Kunming Air), as well as Singapore lounge when flying Silk Air (which you would consider not so far from SQ in terms of service level).