Pemantle's stochastic covering conjecture for NA+ measures

Let $\mu$ be a probability measure on $\{0,1\}^n$. Say that $\mu$ has the stochastic covering property (SCP) if, for every coordinate $i$, the conditional law given $\eta_i=0$ stochastically covers the conditional law given $\eta_i=1$. Pemantle's SCP conjecture. NA+ implies SCP. The source presents this as another conjecture disproved by the same counterexamples used for the preceding NMP conjecture.