Section 4 definitely starts with an actual audio recording. But it ends with Figure 7, which shows the relationship between all possible keys and their simulated sounds. The simulation was "based on real-world acoustic data", but figure 7 is not a property of a single actual recording, it is a property of all simulated recordings.

You could still be right. I've been reading again, and I'm having a hard time telling apart statements about how their tool works in general, vs. statements of a particular test of it.

If they actually tested this thing end-to-end, I would expect to be able to answer (i) how many actual key recordings did they test it on?, and (ii) did it work? Was the actual key found among the 3 (or however many) candidates?