O'Neill's Möbius-function bound for regular Tesler matrices

Let $A\in\T\left(\mathbf{1}^n\right)$ and let $\mu$ be the Möbius function for the corresponding Tesler poset. O'Neill's conjecture.

$$\left|\mu\left(\hat{0},\\,A\right)\right|\leq n!$$

This conjecture concerns the growth of Möbius-function values in the Tesler poset and was posed in the context of asymptotics for regular Tesler matrices. The supplied text gives no resolution status.