Does the CPF own our personal data?

According to reports, a single mother’s identity which she had wanted concealed has been outed by the Central Provident Funds Board (CPF)’s Facebook page.
While I can understand the CPF wanting to put forth its side of the story, could it not have done so anonymously?
The CPF is a big and powerful body while Ms Soo (not her real surname) is but a private individual. Being publicly named by such an influential body could lead anyone to feel exposed and vulnerable. Could this move to publicly name Ms Soo be construed as a means to silence criticism and queries?
In other words, could other individuals with questions or complaints be unwittingly intimidated into silence out of fear of being publicly named? Could this potentially affect the CPF’s ability to improve and innovate if members of the public are too scared to ask questions?
Without going into the merits of Ms Soo’s complaints, it is worrying that a public body feels it has the right to publicly name individuals. Even if not the intention, could this not be construed as a state body bullying an individual? Based on reports, it would seem that Ms Soo is not the only individual who has fallen victim to this public naming.
The CPF could have easily issued a statement of clarification using the pseudonym instead of her real name. Was the making public of her identity a mistake or deliberate?
If it is the former, an apology is due. If it is the latter, there ought to be a public discussion as to the protection of their data by public boards.
As private citizens, we give our personal data to government bodies in the course of our day to day life. By giving such personal data, do we then waive our rights to such data? I would think not.
While public bodies may have our data, it doesn’t stop being our data. It doesn’t automatically become owned by such body to do as it pleases. If we give our data to a particular body for a specific purpose, that body has to seek our consent before using such data for anything outside that specific purpose.
In other words, did the CPF have the right to publish Ms Soo’s identity? Was it their data to make public?
Minister for Communications and Information S. Iswaran had said in Parliament in earlier April this year, that the government is not governed by the Personal Data Protection Act (PDPA) because there are fundamental differences in how the public sector operates compared to the private sector.
He noted that public sector agencies have to comply with Government Instruction Manuals and the Public Sector (Governance) Act (PSGA).
He argued that collectively, these provide comparable, if not higher, standards of data protection compared to the PDPA.
But with how CPF Board is handling the data of its members, one has to question if what the Minister said holds true.