Normality conjecture for packing-property Rees algebras

Let $S$ be a polynomial ring and let $I$ be a squarefree monomial ideal with the packing property, meaning that every minor of $I$ satisfies the König property.

Packing-property normality conjecture. The Rees algebra $S[Iz]$ is normal.

The text says that the algebraic packing conjecture reduces to this assertion using stated results on normality and the packing property; it does not state that this reduced conjecture has been resolved.