The word "direct" is carrying an awful lot of weight in that sentence. The Catholic Church (as well as the Protestant and others) are very responsible for, or at least implicated in, many horrible things in the last few hundred years alone: - signed off on the slave trade for hundreds of years (even gave excuses about how that was God's will) - during World War II they promised to hide many Jewish children, only to subsequently steal them from their parents arguing that "they are now Christian, it would be a sin to give them to Jews" - the inquisitions - were the justification for so many wars (conversion by the sword) - have long been a tool of repressive governments, arguing that it fell under "obey your father" - in the U.S. many churches, including the Catholic Church have preached that voting for one party (Democrats) is a sin (often about abortion, but other topics have been raised)

In general, the Church's political power has waned over the last 500 years or so, but there are an awful lot of calls from Republicans saying that this is where we have gone wrong.

One only look to the political donations of Opes Dei (Catholic branch dedicated to getting Cristian influence over the "Lay" sphere) to see them as major power players today. The Heritage Foundation (main writers of Project 2025) are intimately bound with the organization. And Chief Justice Roberts is also associated.

So they may not be "direct" rulers, they are major power players.