This story is obviously satire. Meaning, it is a lie that tells the truth.
Is it though? What is it satirizing? Is it satirizing the idea of water and carbon based life? How does that tell any truth?
I think basically the humor is how unimpressed they are with a Sagan-style sense of wonder at the cosmos that is implicitly treated as the human perspective, how bleak it would be if true. The aliens ridiculing that is funny, and the actual bleakness of it is funny too.
I think it's (partly) satirizing how we feel about ourselves as the apex beings, and as explorers of the cosmos and colonizers. What if we are actually quite subpar, and the actual apex beings in the universe find us so unlikely and disgusting that they prefer to pretend they are not there, thus giving an answer to Fermi's Paradox? They don't want to conquer us, they don't want to have anything to do with us!
But of course, it's also satirizing this alien-as-a-bug idea, so common of early scifi, that the alien is a disgusting mess of antennae or simly appendages. What if we were disgusting to enlightened aliens?
What we can absolutely be sure of is that Bisson wasn't making fun of meat or the human brain, the thought that apparently irked the topmost commenter.
"Oh god, you're right! They're all just tiny pieces of rubber and silicon, transistors and circuits all crammed chaotically together! How horrifying!"
The story mentions some "official rules". Consider that we also have official rules and behaviour that does not obey them.
I dare suggest your own view might be reductionist.
It might be that this alternative cosmic sense of "normal" is not a real thing (meat may prove to be more cosmically normal than machine at the end of the day), but the sense of wonder in response to something as ridiculous as a brain, in its capabilities and its design, is a real feeling that the story is appropriately trying to evoke.
First, it's a humorous piece.
Second, it's as much a critique of the aliens as of the humans. The aliens are also depicted as clueless about what makes human life interesting, and even shown to be petty in the end. Their behavior is entirely "human", so if they are criticizing humans for it...
Teacher: "Photosynthesis makes energy from water, CO2 and light. The mitochondria are the power centers of the cell."
Grade-schooler: "How do they work?"
Teacher: "Um. Um..."
Modern scientist: "Quantum entanglement and tunneling. We don't really understand any of it."