Etingof's generalized Benson conjecture for semisimplified representation categories

Let $p$ be a prime integer, let $G$ be a $p$-group, let $\Bbbk$ be a field of characteristic $p$, and let $\overline{\operatorname{rep}}(G)$ denote the semisimplification of the tensor category of finite-dimensional representations of $G$ over $\Bbbk$. Let $\mathcal{C}$ be a tensor subcategory of $\overline{\operatorname{rep}}(G)$ equivalent to $\operatorname{rep}(G')$ for a finite group $G'$ whose order is coprime to $p$.

Generalized Benson conjecture. Every prime dividing the order of $G'$ is less than $p$.

This is Etingof's proposed generalization of Benson's conjecture to arbitrary primes, formulated through tensor subcategories of semisimplified representation categories. The supplied text says that the naive assertion that every $p'$-representation is $p'$-invertible fails for $p=3$, while the generalized conjecture is presented without a resolution.