My D’s college prep HS was Catholic and there were definitely strong ties to some of the Catholic colleges, including some of the heavy hitters. Administrators and teachers were often graduates of those schools and definitely could give more strategic advice to students applying. IMO, it’s similar to boarding schools that have strong ties to certainly colleges. The GCs are more familiar with those schools, have better data on who gets accepted, and the colleges themselves are more aware of the high school’s rigor/reputation. Often times the HS’s mission and service requirements better align with the college as well so a student with maybe slightly lesser stats, looks like a better fit.
That said, my kid on paper thought some of the Catholic schools were going to be the perfect match…until we stepped on campus. Finding out that there would be 4 more semesters of theology, philosophy, and other mandatory gen eds, with a much different emphasis than what she was looking for, ended up being a huge turnoff.