You are thinking about one child. The school is thinking about maybe a few hundred but the LA is thinking about thousands and, at LA level, its focus is on funding and future place planning.
By keeping him on roll with the Year 1 cohort, the school is telling the LA that they (LA) will need to have a space for him at secondary school (whether at mainstream or special) in the academic year when that cohort transfers, not the following year.
For one child, this may not seem to be particularly relevant, but multiply it up by the numbers of children potentially involved, who could be dropping back at different stages in their school careers, and it can cause huge issues with there not being enough places in the right schools.
There can also be difficulties when these then young adults reach school-leaving age and can choose to leave without completing their secondary education or, if other agencies are involved (likely if there additional needs prompting the cohort change), they potentially fall into a gap between child and adult services as they are too old for children’s services but adult services don’t work with schools.
Nobody is lying. He is on roll in his true chronological year group. The issue is about how to best meet his needs, and the school clearly feels this that next year this by him continuing to access the Reception curriculum. This is not going to be a permanent solution (he can’t stay in the Reception class forever) so his parents should be working with the school and the LA through the EHCP review process to plan what future provision should look like for him.