If you are only puzzled by the ‚as if‘ notion: I assume this is just a modest and careful expression. We cannot know if the nervous system or living beings in general really follow the FEP and whether information theoretical concepts and thermodynamics really line up. Yes, the formulas are the same. Yes, we can derive a heuristic proof (Karl‘s words) from simple, quasi self evident principles. So it looks as if this works out and suggests that FEP explanations are useful - especially in comparison to our previous models. If a system behaves as if it does X you could also claim it does X. However, this requires further evidence and could be even a metaphysical question.

One additional example, Karl goes on suggesting that the nervous system recapitulates a deep hierarchical causal structure because the world is structured in this particular way. (This leads to the notion of a Markovian monism.) However, I like to think about this also in the weaker as if version. There could be other reasons why our nervous systems needs to model the external world in this hierarchical fashion (e.g., computational costs, encoding of complex probability distributions by simpler distributions). So it appears as if the world is isomorphic to the way we model it. Now, you have to decide if this is truly the case and based on your own choice you will land somewhere on the realism-idealism spectrum.

That is why I like the as if notion. You can decide for yourself to what degree you want to commit to the theory and still have something useful and relatable to work with.