The paper (at http://arxiv.org/abs/0902.1994) does offer some justification for the identification of B and C, or rather points at the work of someone else who allegedly does so.

"The completeness of the particle's geodesic in the spacetime of the Einstein-Rosen bridge in the Kruskal coordinates can be explained if we note that both coordinate pairs (-U,-V) and (U,V) mathematically correspond to the same coordinates r,t. Rindler suggested that both coordinate pairs (-U,-V) and (U,V) physically represented the same coordinates r,t, i.e. region III is identical with region I, and (interior) region IV is identical with region II; the Kruskal spacetime is elliptic. In order to represent the Einstein-Rosen bridge in the Kruskal coordinates, we need to impose Rindler's elliptic identification of event antipodes only on the line V=U, i.e. only the two antipodal future event horizons are identical. After the particle reaches the event horizon of an Einstein-Rosen black hole at point B, it moves from point C, which is identical with point B, to point D, which is related to point A via the transformation (2) of the isotropic radial coordinate r. As the particle moves from point C to D, the proper time tau increases, while the coordinate time t decreases (runs in the reverse direction with respect to observers in region I). This reversion does not cause any problems, because it occurs after t -> infinity, so observers in region I never see it."

I know approximately nothing about general relativity so shan't attempt to comment on the physics of this, but I have to say that there are a bunch of stylistic features that to me strongly suggest an author who isn't thinking very clearly.

A bit of googling for the Rindler reference brings up a snippet from "300 years of gravitation" by Hawking and Israel:

"Since it is, indeed, 'hard to believe that every mass point should have the effect of splitting the universe in two, thus necessitating a second copy of ours' (Rindler, 1965), the elliptic interpretation was resurrected six years later, with varying degrees of reservation, independently by a number of authors (...), but was soon abandoned. Quite apart from the conical singularity there were obvious problems with causality which proved to be insurmountable."

With, again, the caveat that I know scarcely anything about general relativity, my understanding of this is that the bit about not splitting the universe in two is a reason in favour of this "elliptic interpretation" (saying that certain pairs of points in a particular model are actually the same physical point) but that for other reasons -- that singularity, and the "obvious problems with causality" -- the interpretation was abandoned. In the particular context of Popławski's paper, it seems like that singularity might correspond to something with some physical significance, and the causality problems -- IIUC, the point is that if you identify (u,v) with (-u,-v) everywhere then it's easy to make closed timelike loops, so that you could keep going "forward" in time and end up back where you started -- might not matter because the black hole is "in the way" of all the loops you could make. It all seems a bit dodgy, though -- but, I repeat, I don't know anything and you probably shouldn't take much notice of anything I say.