In the same way, when the bank robber says that he was just withdrawing his own money, we do not accept that the bank robber has authority to declare "what is rightfully his money".
But the practical answer is, under Westphalian order whose principles are enshrined in UN Charter (again the organizing order post war), PRC has authority to declare whatever she wants within her domestic jurisdiction, of which Tibet and Taiwan is formally recognized to be part of. UN has no position on legal/procedural merits PCA/UNCLOS ruling for SCS. That's a messy situation that gets resolved same way all territorial problems in Westphalian order gets resolved in lieu of treaty/accord that formally assigns ownership, territorial control with lots of force. So Chinese authority is derived from the same post war order as everyone else.
And private persons with human rights have the authority to name territorial conquest by its rightful name.