Actually that's what their section 6.3 is all about, how if you sent an observer inside the event horizon measurements could influence the outside.

It just admits that the feasibility of this is ridiculous with my favorite line of the paper:

> Physically this seems absurd, as it allows a measurement inside a black hole to produce a record which stays outside, but we are not claiming that any effective-description observer could actually implement this unitary.

But I agree that there's a big difference between the plausibility of measuring the 'stuff' vs it's spacetime configuration - that was a great point.