There are only two "private schoosl" in Memphis that cost over $20k (MUS & Lausanne) and yes they do provide tuition assistance for athletes as well as very strong academic students. However, at MUS-no one rides for free-all must have some skin in the game. MUS in particular has the same graduation requirements for all students. Honors & AP classes are available for all students that qualify but even the standard classes are still quite challenging. Regarding, MUS, despite the rumor mill & hearsay, most would be surprised at the number of "perceived" athletes on financial aid that actually are. Many pay the full boat and most are pretty good students. I know this because I have two sons there.
As for Lausanne, I cant shed a whole lot of light but I can say that they decided that they wanted to have a top notch championship football program. Enrollment increased and sure enough 2-3 years later, they now are the reigning state champion n their division. In addition, it is my understanding that they are designated as the "at large" private school-meaning if your private school does not offer football or if you are home-schooled, you are eligible to play there.
There is at least one private school in town that does have several different graduation "tracks" to accommodate for varying levels of academic capability. Overall, the perception of rampant recruiting & scholarship/free tuition for athletes at the larger private schools is not overly accurate. Yes, it occurs but not to the level that many would like to think.