The vast majority of DLS and other Catholic high school kids come out of Catholic elementary and junior high schools, many of which have highly-organized sports programs, much more so than public schools tend to have. Watch, say, a 7th-grade hoops game in a Catholic league sometime, and compare it to the ratball seen in a typical 7th-grade public-school game. For that matter compare public v. Catholic 4th-grade games... By the time they get to high-school age, they are well ahead of most public-school kids in terms of fundamentals, discipline, mindset, and training.
Since there are no Catholic high schools in the Livermore/Pleasanton area, these same well-trained Catholic kids from there tend to choose DLS, or maybe St. Mary's of Stockton, or Central Catholic of Modesto. So, those and other Catholic high schools everywhere tend to get accused of "recruiting" when they are in reality just receiving the kids that are already in the Catholic system in nearly all cases.
For example, I remember one time a few years back seeing a DLS hoops roster that showed where the kids came from... In that case, ALL of DLS's varsity hoops players had come out of the area's Catholic jr. high schools. While I'm sure there are occasional exceptions, my guess is that this is likely the case most the time, at DLS and other Catholic schools.
So, those who complain about losing "their" area kids to Catholic high schools 30 miles away are in most cases complaining about "losing" kids that are already gone and have been ever since they first enrolled at a Catholic elementary or jr. hi.
This observation comes from a non-Catholic, btw... I didn't go to DLS or any other Catholic school, either. I'm just stating an opinion based on what I've observed at games over many years...
btw, I just noticed at calpreps recently that there is a Catholic school in the works for Livermore, opening date to be determined. I have absolutely zero idea how far along this new school is in development; I don't even know if a shovel has hit the ground yet, nor what the planned size of the school will be. If/when this new school opens, it'll be interesting to see what happens in East Bay sports if that new school turns out to be a "player"...