Extreme coherent laws are 2 by 2 laws

Let $\mathcal{C}$ be the compact convex set of coherent probability laws of $(X,Y)$ on $[0,1]^2$, and let $\operatorname{ext}(\mathcal{C})$ denote its extreme points. A law is a $2\times2$ law if $(X,Y)$ is supported on at most two values of $X$ and at most two values of $Y$. Extreme-law conjecture. Every law in $\operatorname{ext}(\mathcal{C})$ is a $2\times2$ law. Characterizing the extreme coherent laws is presented as an open problem, and the source gives no resolution of this stronger particular assertion.