Tinder,
I think the way to think about it is that for every child who DOES get funding, through PP or EHCPs / statements, there will be a large number of children who don't quite make the criteria.
So a grammar school with very low %PP (say 2%) and very low % of children with EHCPs / Statements (less than 1%) will not only have very few of these funded children, but also a very small number of those 'non funded' children whose needs are not quite as great,.
In addition, those children at grammar schools with SEN or in receipt of PP will be 'fairly simple' cases - so eg. the SEN is likely to be e.g. HFA, or sensory impairments, not complex behavioural needs complicated by chaotic family backgrounds and poor housing. The PP may be those with a low income but not e.g. very poorly housed refugees with no English and a parent in a detention centre, or a child living in a family where all adults have issues with substance abuse.
So the grammar school will indeed get lower PP funding, and lower funding for SEN pupils, because they have a lower proportion of that 'visible and funded part of the needs iceberg'. However, the non-grammars will have many more complex cases included in their higher percentages of SEN / PP AND will have a much larger proportion of that 'don't qualify for money but do have addition learning or social needs' invisible part of the iceberg.
2.9% of all children have an EHCP, for example, whereas 14.6% have SEN. A grammar school with 0.2% 'funded' pupils will probably only have 1.5% 'SEN pupils in total'. A non-grammar with the national average percentages will have 10x more of each, and likely to be more complex cases.