your school will be dealing with the student they have in front of them, not the bits of paper raining down on them from private assessors, as will every school.
What you need to understand is that it is only a certain class of parent that gets a private assessment done, or even an NHS one.
I have said this before on threads like this. In families were a child has genuine ADHD, and a parent also does, then the situation that child is in can be fairly chaotic. Unlike rich, privileged middle class sufferers and parents, scraping around for evidence of difficulties, and getting assessments done.. the children who suffer the worst from ADHD, and have a parent who also suffers, are less likely to have employed, wealthy parents with income to waste of private assessments. They are more likely to come from homes with divorce, unemployment, homelessness, drug use, parents in prison, etc.
ADHD can be a devastating disability, which has a massive impact on life chances - the worse the symptoms, the more the impact on life chances, the less a parent is able to seek an assessment for their child
These are the children that need the most support, and are the least likely to have a diagnosis, that is why NO SCHOOL bases support on diagnosis - because the children who have the worst problems are going to be least likely to have a diagnosis.
So school support is based on the problems and symptoms that a child is presenting with, not the bits of paper they come with.
I am sure you can see how this makes sense.