My thoughts are ...... that this line of argument is unlikely to get you anywhere at an appeal.
The panel is going to accept that Buckinghanshire LA has properly administered the process with NFER - unless there is evidence to the contrary (and that's not easy to come by!).
If you are unhappy with the outcome, the onus is on you to produce evidence of very high ability/extenuating circumstances, sufficient to enable the panel to overturn the LA decision.
That is how the appeal is conducted. I'm afraid you do not get the benefit of any doubt.
Just my twopence worth ........