it's right there in your post. What is "second grade" math, "3rd grade level," etc., if not a one-size-fits all label?
Grade levels are based on age. Learning expectations for that age are based on a wide variety of factors. Sometimes when you hear someone say "__th grade reading level," it's based on the grade level book in an adopted curriculum. In that case, the publisher, with some influence from CA and TX, decided what constitutes "grade level reading."
Sometimes it's based on some purchased program that assigns a level; like Accelerated Reader. The number of people who will run around saying things like "my 2nd grader reads at a 9th grade level" amaze me, since when asked if their child could actually read well enough to process high-school level material, they blink and say, "Well, of course not!"
It could be based on state standards, which, until CCSS, were different in every state. That's the assumption by tptb that everyone at a "grade level" can learn the same amount at the same pace. While there is a constant mantra to "allow more time" when necessary, time is one thing that we cannot manufacture more of.
That said, I'm glad that you found a school that is differentiating for your child. To help schools become more flexible with different groups, I suggest that we first end the standards and accountability movement that pressures schools to focus so narrowly on "grade level" standards and tests.