Uniqueness of a tropical variety from its tropical Chow hypersurface

Let $\Sigma_1,\Sigma_2\subset\mathbb{R}^{n+1}/\mathbb{R}$ be pure $(n-k-1)$-dimensional tropical varieties. For a tropical variety $\Sigma$, let $Z_\Sigma$ denote its tropical Chow hypersurface. Tropical Chow uniqueness conjecture. If

$$Z_{\Sigma_1}=Z_{\Sigma_2},$$

then

$$\Sigma_1=\Sigma_2.$$

This assertion is false when the equality is interpreted as equality of sets rather than equality of tropical varieties, so the conjecture is refuted in its set-theoretic form.