Read again -- I'm saying that it does happen, but it's not something that you can count upon. It's not something that works out for everyone. Perhaps you were the "target demographic", and that's great for you. But having taught high school seniors for 17 years and having watched over 2000 students leave my classroom headed for higher education, I assure you that it's a rather rare situation. Private schools aren't falling all over themselves to offer inexpensive placements to students, even top students.Our experience was a bit different, so don't discount the scholarship offers to private schools!!
Look into it, hope that this -- along with other scholarships -- come together for your student. But don't "suicide it". That is, don't look into this and only this. Don't bank all your hopes on this rather rare opportunity, which may or may not come your way. Investigate this AND other avenues.
I've seen students get these placements, but I've seen more students go to expensive schools at full-price. For what it's worth, I suspect that my oldest daughter is going to receive offers like this; I think she, too, is the "target demographic". I doubt my youngest will have any chance of this type of scholarship; though her grades are good, she lacks the well-roundedness and the leadership spark that my oldest has in spades.