Borovik-Burdges conjecture on strongly real elements and Cartan subgroups

Let $G$ be a simple ranked group, and let $C$ be a Cartan subgroup, that is, the centraliser of a maximal decent torus. An element is strongly real if it is a product of two involutions. Borovik-Burdges conjecture. There is no such group $G$ in which every strongly real element lies in

$$\bigcup_G C^g.$$

This is posed as an unresolved exclusion statement: the authors say that, despite attempts, they could not prove it. The issue concerns whether Cartan-subgroup conjugates can contain all strongly real elements in a simple ranked group.