Sturmfels–Sullivant degree-bound conjecture for group-based models

Let $G$ be a group and $T$ a tree. The group-based model associated to $G$ and $T$ has a defining ideal of phylogenetic invariants.

Sturmfels–Sullivant's group-based degree-bound conjecture. For any group $G$, the ideal of the group-based model is generated in degree at most $|G|$ for any tree $T$.

This generalizes the 3-Kimura degree bound, replacing the bound $4$ by the order of the group. The supplied source presents it as a generalization due to Sturmfels and Sullivant, with no resolution evidence provided here.