Fish [that] fish eat [habitually] eat [food].

OK, that explains fish fish eat eat, but what about fish fish fish eat eat eat?

(Now there's a sentence I never thought I'd be typing today.)

Just extend it.

(Fish [that] (fish [that] fish [habitually] eat) [habitually] eat) [habitually] eat [food].

Fish fish fish fish fish eat eat eat eat eat!

I don't think English works this way. The Buffalo and have/had examples are clearly valid (if extreme) sentences and their meaning leaps out once you see the trick. "Fish fish eat eat" does too, and so would "Fish fish eat eat fish". But you can't arbitrarily nest these clauses, and "fish fish fish eat eat eat" doesn't click for me. The suggested analogy, "Mice cats dogs chase eat sleep", seems accurate as an analogy because it's invalid in the same way; that is, "Cats dog chase eat" is clearly ok, but the next step of nesting is not. It would be interesting to pin down the reason.

I agree that it's no longer english as she's spoke, but it is ultimately comprehensible with difficulty. It's harder to unpack deeply nested clauses; human beings have trouble thinking on more than one levelf of the stack at the same time. Whether that counts as grammatically correct is a matter of definitions; I'd say it does, but it hardly matters.

Even with the interspersed words I still can't make sense of it.

Unlike, say, buffalo [that habitually] buffalo buffalo [habitually] buffalo buffalo [that habitually] buffalo buffalo.