Non-revisiting Conjecture for simple polytopes

Let $P$ be a simple polytope, and let $u$ and $v$ be arbitrary vertices of $P$.

Non-revisiting Conjecture. There is a path from $u$ to $v$ which at every step enters a different facet of $P$.

The source presents this as an equivalent formulation related to the Hirsch bound. The supplied material gives no resolution status for this formulation.