Thank you for that link - it was very helpful. Summarizing:
The same problem would exist for the electric field from a charged black hole. However, static fields don't need propagating photons to establish them, so you don't have to get photons from inside the black hole in order for the electric field to be established outside.
The same would be true of gravitons. But one respondent indicated that general relativity can't do a second quantization like electromagnetism, and therefore gravitons are... suspect? Impossible? Not proven? It wasn't clear to me how strongly to take that statement.