Tverberg's theorem for max-T convexity

Let ${\mathcal B}^d=[0,1]^d$ be the $d$-dimensional box equipped with max-T convexity, and let $X$ be a set of $(d+1)(r-1)+1$ points in ${\mathcal B}^d$. Tverberg's theorem for max-T. There are $r$ pairwise disjoint subsets $X^1,\ldots,X^r$ of $X$ whose max-T convex hulls have a common point. This is the max-T analogue of Tverberg's theorem, presented immediately after the topological version; the source provides no resolution evidence for the stated claim.