Mystery solved

With the help of the Picture This plant identification app, I discovered that the trees in Eben and Luca's school playground that have puzzled me are 'New Zealand Broadleaf' (or 'Griselinia Littoralis', which sounds much more exotic). They're quite robust evergreens. Although they sit in an area of plastic grass, they are proper living trees. A close-up view revealed an occasional brown leaf, by way of proof.
Somewhere in the school's history, there's been an active and enthusiastic gardener (in other areas of the school site there are apple trees). Their legacy lives on.