That health study is pretty interesting.
First, Croatia is only mentioned in passing as a footnote as having comparable rates to the US.
Croatia, a modern european country (not a third world country as was suggested) has universal health care and very good outcomes.
The study examines why the US has worse outcomes than four European countries, being Austria, Finland, UK and Belgium. It notes that it can be impossible to do these comparisons for some countries due to inconsistencies in reporting criteria. But in these cases they were able to do meaningful comparisons.
It was found there is no meaningful difference in neo-natal death rates, deaths shortly after birth. The differences were accountable to post-neonatal deaths, generally after the child went home from the hospital or midwifery center. They examined if the higher incidence of post-neonatal deaths might be because the US is better at saving neonatals and thus just shifted inevitable deaths to the post-neonatal window. That was found not to be the case.
Eventually the differences came down to education levels of parents. Highly educated americans have the same rates as highly educated europeans. But americans with very low levels of education have much higher post-neonatal death rates than europeans with the same level of education. This is the main factor in the difference.
Most european nations have nurses make free home visits during the post neonatal period. It was speculated that implementing a similar program in the US might address the higher post neonatal death rates among the most uneducated.