The onus is on the people making claims in general. In this case someone (the journalist?) made a claim that "spartans didn't kill `weak' babies", so the onus is on them.
A specialist in the area could just say “appeal to authority” and they’d be right. The actual peer reviewed articles and books would require evidence.
But those articles and books wouldn’t be accessible to the average reader.
So the journalist is summarizing those arguments, but in the process reducing them to an appeal to authority - which is completely fine.