Baby Swap: The right thing?

Here's a story that supposedly happened outside of the US.

Two mothers come to give birth at their local maternity ward. Both do, both mothers survived but only one baby survives.

The mother who lost her baby is resting and speaking casually to whatever staff is with her and explains that she had been trying to have a child for a long time. Obviously she's very upset. The father is not in the room when this happens apparently.

The second woman who's baby survived has four other kids and can't support the newest. The father of her child is unhappy about another kid and didn't bother showing up because he was working. (Not that this wasn't partially his fault but at least he was trying to support them I guess)

So what happened is that the staff happened to have not charted anything yet, which I find odd but again it's not a US hospital and could be a tiny rural clinic for all we know. They put the two women in a room to "talk about something". The baby is given to the mother of the child who died and their charts are swapped. In other words, making it appear the woman with the four prior children was the one who had the stillborn instead.

The debate is if this is ethical or should never have happened. She didn't adopt this baby, the baby will assumedly have no biological medical records from it's parents, but they both found a quick solution to their problems. Assuming they wouldn't be caught -do you think this was ok to do?