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The paper this post appears to be referring to is Tom Hutchcroft's 2026 article Are there non-trivial theorems about all finitely generated groups? The official abstract says the paper discusses "potential counterexamples" to the meta-mathematical question in its title, not a proof or vindication of the Gromov aphorism. In the paper itself, Hutchcroft says the goal is a "light-hearted" critique of the aphorism and then gives examples of non-trivial properties that hold for all finitely generated groups.

So the post reverses the paper's actual thrust: the paper is not a vindication that every universally true group property is trivial, but an exploration of why that slogan is too crude and has counterexamples. The post also overstates the slogan itself: the paper formulates the aphorism for finitely generated groups, not for all groups.