@UKUSMum I think that I am that 'someone'. My comment referred to avoiding generalisations and was based on the fact that (a) Freedom of Information requests do not apply to schools (this is a frequent misunderstanding that I have seen in other threads - not here, hence why I did not refer to your previous comment as you had not mentioned it).
As for the providing feedback on tests being an obligation, it figures nowhere in the application form or in the admissions policies that the schools publish in their websites, as at least in the case of the schools that we have applied for. You might, of course, want to check yours (as said above, I shy away from generalising).
I find rather strange that statement from your DC's HM about us paying the schools we are applying to test our children - my understanding is that we are paying them to enter an admissions process, which is rather different. In that context, worth noting that a school providing feedback is rather different to a school providing the scores on the tests.
On an anecdotal basis, I know of examples of parents that have asked for feedback and got a rather standard line on 'there were, on the whole, stronger candidates'.