The irredundance conjecture for direct products of complete multipartite graphs

Let $H_1,\ldots,H_n$ be complete multipartite graphs, and let $G=\prod_{i=1}^n H_i$. The independence number $\alpha(G)$ is the largest size of an independent set, and $\operatorname{IR}(G)$ is the maximum size of an irredundant set. Irredundance conjecture.

$$\alpha(G)=\operatorname{IR}(G).$$

This removes the assumption that the factors are balanced and is presented as a strengthening of Burcroff's conjecture. The source does not provide a resolution of this broader statement.