Do surface currents (in EM scattering) really exist?
It's just a question of levels of models.

At any given level, its abstractions 'exist', in the sense that they're what you do the sums with. So yes, surface currents exist in that model. If you know what underpins that model, then you can explain those abstractions in lower terms. 

The lowest level model we have is quantum mechanics. If your maths is up to setting up the wave equation for the reflection situation, then go ahead. I think it's generally agreed that QM is not necessarily the lowest level model there is, as it doesn't agree with the other good model, GR. But, it's all we have at the moment.