Here's a scenario I've seen played out several times during my career...
The student has a learning disability and has been struggling with academics in the public schools for a considerable period of time, say two, three, or four years or so. The student, parents, and teachers are frustrated that John just can't get it due to the learning disability.
Then, one day, the parent says, "That's it!" and up and enrolls the student in a private school.
Note: learning disabilities "aren't allowed" in many private schools (i.e., there is no special education and no Section 504).
Guess how this story inevitably ends?
The student somehow... does just fine!
It turns out that the student didn't have a learning disabiity at all... s/he only needed to start doing their job as a student -- the student chose to succeed at least in part because parents were paying $3000 a month for the private school!
I wonder what would happen if all students with SLD in public schools were sent off to private schools (I'm not advocating that, by the way)? I guess my questions always boil down to the same bottom line... what if there was no special education? I bet most students would somehow find a way to succeed [if given the chance].