While you are certainly right on historical facts and thus the implied legitimacy of RoC, the reality is when a news agency or the public in general mentions the term China, by default they mean P.R. China. Therefore, the quoted sentence is merely describing (not agreeing) with the POV of said China, which is not that ridiculous to a neutral third party.
Taiwan is a self-governed sovereignty by most accounts, with its own economy, political system and military. It does not have mainstream international recognition from other countries however, most due to P.R China's pressure. For instance, Taiwan is not part of UN, major nations like US failed to acknowledge it as a independent country due to their reluctance to upsetting mainland China - who frequently threatens open war for such 'treacherous division of the one China'. Therefore, there are only 30 or so countries openly supports Taiwan's independence.
The morality of Taiwan's sovereignty debate obviously takes the narrative of a oppressive dictatorship and its democratic neighbor, but to claim Taiwan or RoC as the legitimate government of China and label P.R. China as the illegal, rogue ruler is far-fetched in the current world's landscape; after all the latter has taken control over the China for over half a century, wield much more political and economical power, and is widely acknowledged as a legitimate country for decades. It's almost like saying US is not a legitimate nation, rather ilegal rebellion against the Great Britain ever since some two hundred years ago.