Self-inductance of toroid of rectangular cross section (N=windings?)
It's just a (confusing) way of saying 'stick to the simple calculation of flux in the core, don't worry about flux in the air'.

The inductance of a wound toroid consists of the sums of two contributions ...

a) The inductance due to the field through the core

b) The inductance due to the field in the space round the wire

The inductance due to the core dominates the total, increasingly so as the core relative permeability increases. It's easy to calculate, the magnetic path length and cross section are sell defined. This inductance is what most people would stop at when they want to calculate the inductance of a wound toroid. This inductance is the same whether the wire is wound uniformly tightly to the core (closely approximating a thin homogeneous current layer), or is wound more loosely, or in a single bunch or bunches on just part of the circumference.

The inductance due to field through the air is small, and almost totally negligible compared to the core contribution for any reasonable relative permeability. It's difficult to even estimate its contribution, calculation of it would involve 3D integrals of Biot Savart. For windings in the form of a thin homogeneous current layer, its contribution is zero, as such a toroid has no external field.