Pemantle's NA+ implies NMP conjecture

Let $\mu$ be a probability measure on $\{0,1\}^n$. Write $\mu_k$ for the conditional measure given $\sum_i\eta_i=k$, and say that $\mu$ has the normalized matching property (NMP) when $\mu_l\succeq\mu_k$ for $l\geq k$ whenever both conditionals are defined. Pemantle's NMP conjecture. NA+ implies NMP. The paper explicitly states that this conjecture is disproved by the examples in its counterexamples section.