Time reversal symmetry doesn’t say that you can time reverse system A while not time reversing system B, if systems A and B interact. The time reverse of a particle falling into a black hole is not a particle emerging from a black hole, it’s a particle emerging from the time reverse of a black hole.
The time reverse of a black hole would not violate GR per se, but there are other reasons (thermodynamic, cosmological, causal complications) that suggest such things probably don’t exist in the real universe.