OP was being sarcastic. “Skin-to-skin” contact with mum is the very first thing they do after child birth, and continue recommending for the entire stay.
You might be thinking of one story that went viral a few years ago, and was amplified by the media. It was successful at generating outrage and so became popular, but it was not correct.
It would only be one of many ridiculous charges in the US medical system. I personally think it's pretty outrageous that one has to pay for medical care while giving birth at all.
So the doctors and nurses involved should just deliver babies for free? Does the free care apply only to standard births, and then they get paid if there are complications? Or is anything involving the delivery plus anything arising from it provided for free?
The central bank prints money (partially offset by tax). Some of that money could go to basic medical care like this, as it does in most other countries.