@AuntieAssumpta, I think her attitude was 'it's nothing to do with anybody else' - they were illegitimate, though, and whilst she inherited a sizeable amount from an aunt, she didn't receive anything from her parents, who were worth pots of money, a few years later, so I do wonder whether there was some of that involved. It also meant that they weren't evacuated (she refused to leave and knew that she'd be expected to do it with small children), with the result that before he was born, my mother was trapped in a bombed out townhouse overnight because nobody knew she was there.
The boy died at around three months old, black and blue all over the torso - I can't imagine the pain he suffered in his little life.
I wouldn't be too sympathetic to my mother, though - she tried to do the same with me to keep Social Services off the scent (one of my older brothers was on the At Risk register due to her behaviour), My father found out and immediately registered me, lying about being married to her to do so. She dumped him, changed my name and avoided all officials until I reached 5 and somebody realised there was another child in the house when checking on my brother.
Secrecy about registering a child can be for 'harmless' reasons and malevolent ones - but the outcome can be at best inconvenient and at worst horrific, whatever the reasoning.
So the people in the OP can get stuffed with their ownership bollocks. The kid needs to exist legally. For its own protection - and social services is more appropriate than the registrar, as that means any previous issues with the parents can be looked at first without them knowing a potential investigation is on the way.