The problem with this conversation is that much of private-school recruiting falls into a gray area. The head coach isn't calling up kids directly and finding out what it will take to get them to transfer or mailing them checks, renting them apartments. He doesn't have to. Much of this happens at the parent/booster level, and the top kids are easily identified and contacted through other activities including off-season leagues and competitive club sports.
Around middle school, sometimes earlier, parents who know their kids are going to ... whatever private school ... call it School A... start chatting up the parents of kids they want to play with their kids, and ascertaining where they might be going. They talk up School A, and talk about financial aid, the great education, etc. They will mention how they know someone who lives in the neighborhood who would be glad to carpool, or just give their kid a ride every day. All rather innocent, but they aren't having the same conversation with Joe Average kid who isn't athletic or a great student.
It's all very murky, but yes, I personally know kids (and/or their parents) in several sports who were contacted this way, and it was pretty much laid out that need-based scholarships were available if they really wanted to go to school A, and that the parents were just SO supportive of all kids at school A, they would help with transportation, uniforms, incidental costs, etc. And this is not just Mullen, it's also Kent, Machebeuf, Regis. I don't know anyone contacted by Valor, but that's probably because it's so new.
Since some of the private schools do excel in certain sports, if your son or daughter wants to be part of a winning tradition, people listen to the pitch. It comes slowly and steadily from people who already know each other through sports, and summer leagues, and church, and top athletes get encouraged to consider School A, B or C by parents and boosters who want to see the school win. They are competitive and want the best kids on their teams.
It's very hard to pinpoint when it crosses the line into recruiting. You can bet there is "recruiting" in the public schools - where there is open enrollment and the student has a choice - if you were in Denver Public Schools and a top basketball player, you'd do everything in your power to enroll at East and play for Rudy Carey. And the top basketball players, who you already know from the Crown or Jam league, and years of YMCA ball, know who you are, and say "we can't wait for you to play with us, we're going to win state this year ..."
If you play hockey, you look at those schools with strong hockey teams ... (that's who was "ahem" recruiting hockey players I knew, or at least letting them know how easy it would be to attend there...) If you play football, and a school that has been in the state championship is interested, you give it a look. Soccer players, tennis players, golf ... the best are all identified by 8th or 9th grade, and high school boosters are in contact, making sure athletes know what their options are.
It's recruiting, but rarely as blatant as people expect. It grows slowly through the relationships already established.