For each uniformity $k \geq 3$, we construct $k$-uniform linear hypergraphs $G$ with arbitrarily large maximum degree $Δ$ whose independence polynomial $Z_G$ has a root $λ$ with $\lvertλ\rvert = O\left(\frac{\log Δ}Δ\right)$. This disproves a recent conjecture of Galvin, McKinley, Perkins, Sarantis, and Tetali.