Black hole singularities do not start right after their event horizon. The event horizon only demarcates where the black hole singularity becomes an inevitable (inescapable) point in all possible futures.
That's not what I was trying to imply, sorry. It's the singularity at the center where GR entirely breaks down, but there's also weird stuff going on below the event horizon (space becoming time-like and vice versa), that aren't present in, e.g. String Theory's Fuzzballs [1] (which, of course, bring their own set of thorough weirdness). So what I was trying to say was that while GR predicts some behavior below the event horizon, a full model of quantum gravity could predict something entirely different, and not only for the area just around the singularity itself but (maybe) up to the event horizon.
[1] https://en.m.wikipedia.org/wiki/Fuzzball_(string_theory)