Conjecture on matroidal 3-colorability of paths

A graph $G$ is matroidally $k$-colorable if, for every $k$-coverable matroid $M$ on the vertex set of $G$, the vertex set can be decomposed into $k$ stable sets of $G$ that are independent in $M$.

Path 3-colorability conjecture. Every path is matroidally $3$-colorable.

The claim is presented as a consequence of the Aharoni–Berger conjecture for cycles together with the subgraph property for matroidally colorable graphs. Its status is not resolved in the supplied text.