Recognition of private autism diagnoses

The spectre of private diagnoses not being recognised by local authorities, or the NHS, is fairly often raised here. The following link gives some clarity on this question: https://www.mindtherapeutic.com/ehcp-private-diagnosis-recognised

It would appear that if the diagnosis was carried out in the approved manner by relevantly qualified people, registered with the GMC etc., it should be treated in exactly the same way as an NHS-funded diagnosis, and that any public body not recognising it is acting unlawfully and can be taken to a relevant tribunal.