But observers can see a black hole grow over time, so does that mean they observe growth without consumption?

> external observers would never

Consider two strongly-interacting freefallers related by a boost colliding and sticking together (like a black tshirt and a floof of white pet fur) close to the apparent horizon.

Consider a freefaller and an accelerated observer meeting close to the apparent horizon. The freefaller here could be distant starlight and the accelerated observer a powerful rocket.

Are you saying these coincidences are forbidden in the vicinity of an apparent horizon (which is locally detectable), or are you distinguishing between the apparent horizon and the (global, but not locally detectable) event horizon?

Where is the point where the t-shirt will remain unsullied by unremovable fur? What light does an outwards-pointing camera on the spaceship see?

Visser [2014] "Physical observability of horizons", https://link.aps.org/doi/10.1103/PhysRevD.90.127502 aka https://arxiv.org/abs/1407.7295 about the variety of horizons about which one should be careful.

The equivalence principle demands that the local free-fall frames on the t-shirt and the fur are both smooth. At an enormous black hole, the curvature is also small (we can make the black hole so large that the curvature and tidal effects are comparable to the surface of the Earth). The result is the "no drama" conjecture, wherein nothing special happens immediately upon crossing the event horizon. Detecting the apparent horizon requires some cleverness to shear apart a cloud of coffee grinds or the like while the components are variously on hyperbolic trajectories (and will escape the region around black hole) and infalling trajectories (which will be stuck below a trapping surface).

The shirt-and-fur will form a single extended object and continue to infall togther. A violation of this would be a violation of Local Lorentz Invariance, which would be beyond known physics, all of which enjoys LLI (and global Lorentz Invariance in the idealized flat spacetime of Special Relativity).

This gets trickier just inside the horizon because of of causal disintegration: electromagnetic interactions from the inner part of an extended object can no longer reach up to the outer part of the extended object. For a time the outer part of the extended object can "catch up", but eventually intermolecular and other forces will fail, such that the tshirt will not experience being furry.

Local physics is local. The tshirt-fur meeting above the apparent horizon may be too redshifted to be visible by various classes of observer above. The electromagnetic radiation from them meeting below the apparent horizon is stuck behind a trapping surface; observers above will not see a furry tshirt.

Generically an accelerated freefaller shooting itself through a horizon will see freefallers as being fast (clocks running fast, high velocities). The effect increases as the horizon is approached, so a camera looking back at distant starlight sees a high blueshift and a focusing into a small region of the accelerated infaller's "sky". One can analyse this in several ways, but the acceleration/gravitation equivalence means the rocketing infaller is not much different from an observer standing still on a planet freely falling into the BH, or alternatively one can consider its suprageodesic in a convenient system of coordinates in a setting like Vaiyda's absorbing null dust. The inwards-accelerating rocket camera sees a blueshift from its own acceleration (because that is equivalent to gravitational blueshifting) and from the falling of the distant starlignt down to the black hole, which will be blueshifted in the backwards pointing camera.

Finally on the inwards-accelerating rocket, we have Unruh/Rindler in play locally (and local is fairly large for an enormous black hole); the Rindler horizon is ahead of them, so the backwards view is not behind the Rindler horizon. They can still receive light from outside. You don't want to collide with anything on an intersecting geodesic if you are this type of infaller, and eventually that includes highly-blueshifted starlight. Sizzle.