Continuity of p-rationality under p'-index subgroups

Let $p$ be a prime, let $G$ be a finite group, let $\alpha\in\mathbb{Z}^{\geq 2}$, and let $M$ be a subgroup of $G$ of $p'$-index. Continuity under p'-index subgroups. The group $G$ has an irreducible $p'$-degree character of $p$-rationality level $\alpha$ if and only if $M$ does.

The source states that this is equivalent to the combination of the continuity conjecture and Isaacs–Navarro's conjecture. No resolution is supplied for this equivalent formulation.