White's symmetric exchange conjecture for matroid bases

Let $\mathrm{M}$ be a matroid, and let $\{B_1,B_2\}$ and $\{B_1',B_2'\}$ be unordered pairs of bases such that the multiset union of $B_1$ and $B_2$ is equal to the multiset union of $B_1'$ and $B_2'$. Farber's conjecture. It is possible to obtain $\{B_1',B_2'\}$ from $\{B_1,B_2\}$ by repeatedly replacing $\{B_1,B_2\}$ by a symmetric exchange $\{\tilde{B}_1,\tilde{B}_2\}$. This is the $s=2$ case of White's symmetric exchange conjecture, also known as Farber's conjecture. The paper gives a counterexample to this assertion, so it is false.