Liu--Xu's Davenport-constant closeness conjecture

Let $\Gamma$ be a finite abelian group. Its Davenport constant $D(\Gamma)$ is the least positive integer such that every sequence of $D(\Gamma)$ elements of $\Gamma$ has a nonempty subsequence with sum $0$. A group-labeled matroid is $k$-close when, whenever a zero basis exists, every non-zero basis can be exchanged for a zero basis by removing at most $k$ elements. Liu--Xu's conjecture. Every finite abelian group $\Gamma$ is $(D(\Gamma)-1)$-close. The paper presents a counterexample to this conjecture, so the asserted bound is false in general.