This is not a full answer, since I don't know the full answer, but it is more than a comment.
My contribution is to compare your question with another, simpler one, and then come back to yours.
1. Observer-dependence of radiation in classical physics
Here is the simpler question (one to which an answer is known). A charged particle accelerating in empty space will emit electromagnetic radiation. A charged particle fixed at some point in a static gravitational field will not emit electromagnetic radiation. Both statements are true---relative to a certain natural choice of reference frame in each case. But, in the first example one could step on board a rocket accelerating with the particle, and no electromagnetic waves would be seen in the rocket frame. In the second example, one could go freely falling past the particle, and in this freely falling frame, electromagnetic radiation will be seen. So what is going on here? Does the charged particle emit radiation or doesn't it?
All of this scenario can be treated with special relativity, and it teaches good lessons to prepare us for general relativity. The main lesson here is that the process of emission and subsequent absorption of radiation is not absolute but relative, when accelerating reference frames are considered, but the state changes associated with absorbing radiation, such as a detector clicking, are absolute. It is the way we interpret what caused a detector to click that can change from one frame to another.
To make the above really connect with your question, note that in my simple scenarios I could imagine a cloud of gas possibly absorbing the radiation in between emitter and receiver, just like in your scenario.
2. To resolve a paradox in observer-dependent physics, first convince yourself about the easiest observer, then seek arguments to explain what the other observer finds
The above principle can be applied to resolve puzzles in relativity such as whether a fast pole can fit into a short barn, or whether a fast rivet can squash a bug in a hole.
3. Unruh effect has two complementary physical interpretations, depending on who is accelerating
Hawking radiation is like Unruh radiation, and therefore it is more subtle than classical radiation. A useful tip from the consideration of Unruh radiation is as follows. Unruh's calculation says a detector accelerating through the vacuum picks up internal energy, equivalent to detecting particles. Now if we look at this detector from an inertial frame, we still conclude it picks up excitation, but we interpret differently: we say the force pushing it provided some energy which got converted into internal energy because the process is not perfectly smooth.
Now I will apply all the above to provide an answer to your question.
I admit I am not sure and the following answer is just my guess. I only claim it to be an intelligent guess.
My guess is that the distant observer observes Hawking radiation and absorption lines. I say this because it is a consistent summary of what seems to me to be ordinary physics, assuming that there is Hawking radiation coming up from a horizon.
So the puzzle is to explain this from the point of view of the freely falling cloud. I think an observer falling with the cloud looks up at his distant friend and notices that his friend is accelerating through the vacuum, and consequently experiencing internal excitation owing to fluctuation of the forces accelerating him. To account for the absorption lines, i.e. the absence of excitation at certain frequencies, I guess (and this is the speculative part) that now the calculation from quantum field theory would have to take into account that the rest of spacetime is not empty but has the cloud you mentioned, and this cloud affects the overall action of the quantum fields in this way. Note, it is not a case of action at a distance (in either perspective), but it is a highly surprising prediction so I think your question is a very interesting one.