External BEM theory explanation help

So I’ve read through BEM theory several times over several years now and there’s something that always bugs me. Perhaps one of you has an intuitive explanation.

The Green’s function for acoustics is simple to understand, it varies with 1/r and it’s harmonic (spherical harmonics).

In an exterior acoustics problem, some points on the boundary will always be occluded to the observer point. I’m wondering how a summation using the “straight line” distance between observation point and boundary point can possibly work? The path length between the points would need to bend around the boundary, but the math doesn’t seem to directly reflect this.

Does the method end up looking more like a spatial fourier transform, where all those Green’s functions add up to encode the boundary?

Anyway, this may be confusing in text form, but perhaps one of you will understand what I’m getting at and have a simple explanation!