I'm no authority, but I love this stuff. I read Dr. Hawking's book "A Brief History of Time", and it was not problematic for me.
My takeaway is that a black hole is a sort of manifold. It would follow that if there is a way into it, and stuff going into it, the stuff must be coming out somewhere.
The question is where that stuff comes out, and in what form, and when, in it's local time frame.
I had always envisioned this hypothetical 'other side' as a white hole. It seems like, since we haven't observed any white holes, that the exits must be elsewhere.