My comment:
(a) What surprises me is that in this news report at least, both KMT (王郁琦: "我们对南海、中华民国所有的相关岛屿跟附属海域拥有的主权") and DPP (张旭成：“因为民进党的人，包括本人，都已经表示台湾应该调整我们对南海领土的主张") uses "南海." These are quotations, not the reporter's words. Back in Taiwan (before 1984), I did not hear of 南海; it was "南中国海."
(b) It is not surprising that DPP does not want South China Sea. In early 1990s, I went to hear a talk of DPP celebrity at Harvard University (to Taiwanese students, in Mandarin), who said many in DPP were considering giving up Matsu and Quemoy (Kinmen) in exchange for a peace treaty with China (which would be unacceptable to China, I later learned).