Nilpotent Borel subgroup conjecture for simple ranked groups

Let $G$ be a simple ranked group, and let a Borel subgroup mean a definable, connected, soluble subgroup maximal among such subgroups. Nilpotent Borel subgroup conjecture. If all Borel subgroups of $G$ are nilpotent, then

$$G\text{ has no involutions}.$$

The source explicitly says this assertion is open when only the definable, connected soluble subgroups are assumed to be nilpotent, in contrast with the stronger known results discussed immediately beforehand.