I think much like the stick, or a Minecraft seed, or other examples of procedural generation, you can get a near infinite amount of results via different seeds

I think much like the stick, or a Minecraft seed, or other examples of procedural generation, you can get a near infinite amount of results via different seeds from a program with a relatively small total size. But you cannot ever get an exact result you want, unless it's already one of the outputs of the algorithm. Much like the key described in your article, it may be possible to get a very accurate result from an AI via a very long and specific prompt. But that long prompt is then where the "magic" compression goes away.