Interesting thread again.
I have DC at selective primary schools - though nothing like Mominatrix's one, since I have never heard of a child who was Grade 8 in an instrument by year 5...as Bobo says, criteria for music scholarships are usually that they are at Grade 5 level in at least one instrument by the scholarship auditions in Year 6.
To help those who wonder what is done at the 4+ selection, the schools do a series of "games" with the children designed to assess a range of cognitive abilities in an age appropriate way. As noted, they are also looking for teachability to some extent, and will observe their interactions in a group setting. A HT once admitted to me that the tests are only reliable from around age 3.5, so difficult to assess the summer borns, but overall based on my own experience they do a reasonable job of identifying the "above average" (say IQ 115 plus).
They do sometimes throw up "false positives" - but of the order of maybe 10% in each year group who end up not progressing to the senior school. I also suspect they result in plenty "false negatives" mostly kids who just develop a bit later or just aren't in the mood to perform on the day.