I don't think this is entirely true. I have seen just as many parents wake up to realize their kid is in 4th grade and has the reading level of a lima bean and then they say "the school has failed my child!" Whereupon they shuttle their kid over to the charter school and continue to not be present or proactive in their child's education and, unsurprisingly, they end up with the same results.

I think that there's a tendency for students who are not succeeding to be moved out of whatever school system they're in to the alternative in hopes of better results.

I 100% believe your mom's experience is true. However, it's the same as my experience as a charter school teacher when we get new students from the public school.