Stanley's reformulation of Kontsevich's polynomial-counting conjecture

Let $G$ be a finite graph with edge set $E(G)$, and let

$$Q_G=\sum_T\prod_{e\in T}x_e,$$

where the sum runs over spanning trees $T$ of $G$. Let $V(Q_G)$ be the zero scheme of $Q_G$ in $\mathbf A^{E(G)}$, let $X_G=\mathbf A^{E(G)}\setminus V(Q_G)$, and write $[X_G](q)=\#X_G(\mathbf F_q)$. Stanley's reformulation. For all graphs $G$, $[X_G]$ is a polynomial in $q$. Stanley showed that this conjecture is equivalent to Kontsevich's conjecture for $Y_G$. The paper's main theorem disproves the equivalent Kontsevich conjecture, so this reformulation is refuted as well.