Navarro–Tiep's conjecture on achieving p-rationality levels at p-elements

Let $p$ be a prime, let $G$ be a finite group, and let $\chi$ be an irreducible $p'$-degree character of $G$. The $p$-rationality level of a character value is defined using the $p$-part of the conductor of that value. Navarro–Tiep's conjecture. If the $p$-rationality level of $\chi$ is greater than $1$, then it is achieved at a $p$-element of $G$; that is, there exists a $p$-element $g\in G$ such that

$$\operatorname{lev}(\chi(g))=\operatorname{lev}(\chi)>1.$$

The source identifies this with the cited conjecture of Navarro and Tiep and does not state that it has been resolved.