The whole point of the article is that private schools get away with things because they're private. If they want to make that claim, then they do have a responsibility to make sure that the facts back it up.
You've built a fine straw man. But in fact, the authors explicitly identify several hypotheses that aren't inherent to (but do correlate with) private schools:
1. "boarding schools, in particular, present unique opportunities for educators to have close contact with students" (yes, public boarding schools exist.)
2. "The schools, many with rich histories and famed alumni, have often struggled to balance the need to respond robustly to abuse allegations with a desire to guard their reputations." (yes, public schools with rich histories and famed alumni exist.)
So the authors specifically aren't saying that the schools "get away with things" soley because they're private. They're simply saying that abuse happens at private schools. Which, regardless of how it compares to abuse happening at public schools, is worth reporting on.
> If they want to make that claim, then they do have a responsibility to make sure that the facts back it up.
1. Your strawman aside, The actual claims made in the article are all well-substantiated or else are clearly presented as hypotheses, not facts.
2. Following this principle would effectively censor a lot of important investigative journalism.
As far as journalism these days goes, this article is excellent. The writing is nuanced but clear, the reporters report back hypotheses about underlying causes that relate to the human side of the story but with minimal editorializing, and the article is even accompanied by a hand-curated data set.