  In recent work, Akers et al. proved that the entanglement of purification
$E_p(A:B)$ is bounded below by half of the $q$-R\'enyi reflected entropy
$S_R^{(q)}(A:B)$ for all $q\geq2$, showing that $E_p(A:B) = \frac{1}{2}
S_R^{(q)}(A:B)$ for a class of random tensor network states. Naturally, the
authors raise the question of whether a similar bound holds at $q = 1$. Our
work answers that question in the negative by finding explicit
counter-examples, which we arrive at through numerical optimization.
  Nevertheless, this result does not preclude the possibility that restricted
sets of states, such as CFT states with semi-classical gravity duals, could
obey the bound in question.
