Yes, your understanding is my understanding, IYKWIM. Around 500 children are invited back as a result of getting around 65 or above out of 80 on the NVR test. The tests were definitely set by NFER, the school tells you this in the invitation letter so why they suggest Athey for practice is a bit of a mystery although there is a commonly held perception that the shop-bought Athey are harder than the shop-bought NFER papers. How hard the paper actually is is anybody's guess as I've never seen an actual paper used in an 11+ exam.
Only 4 types of questions on the Athey papers are used - analogies, series, isomorphic and matrices so the rest of the practice papers are effectively redundant. On the Athey isomorphic papers they ask for two shapes with similarities rather than the one shape asked for on NFER and I think the timing on the NFER papers is more generous - although again this depends on how hard the actual question is.
I heard that around 1800 had applied, this may not be accurate but there was about 200 children at my sons test and this only covered surnames starting with A and B.
I was really interested in your comments re NFER vs Athey papers.
Our daughter has just taken the test in Lincolnshire and the interesting thing was that the actual NVR test was made up of the 4 sections that you described above (16 questions in each + 1 extra giving 65) which are present in the Athey papers, even though the paper was set by NFER.
The schools used NFER practice papers which were similar but contained a CODE section (as usual in NFER) which was then nowhere to be seen in the actual test.
It seems as if perhaps the actual exam was set by NFER in the style of Athey. If this was the case, then the advice to use the Athey test papers was smart indeed!