would they still have to prove the selection review was non-fair and compliant
Strictly speaking, it should be for the admission authority to prove that the review process was 'fair, consistent & objective', not for the parent to prove that it wasn't.
Imagine someone goes through the Bucks Selection Review process and is unsuccessful but later on discovers new relevant evidence (e.g. a learning disability).
In that case, the review panel has done nothing wrong - it couldn't consider evidence that it wasn't presented with.
However, the review might well be found to be unsatisfactory for other reasons (lack of evidence that it was
'fair, consistent & objective').
Incidentally, the admission authority does have discretion to allow a fresh appeal
if presented with significant new evidence that wasn't - and couldn't have been - available for the first appeal hearing.
Although I'm not aware of a similar established arrangement for a review, common sense suggests it's something the admission authority (or LA acting on their behalf) might be prepared to consider, provided the degree of disability is significant.
Very good question - best I can do!