  The moduli space $\bar{M}_{0,n}$ of stable rational n-pointed curves has
divisorial boundary with simple normal crossings. In this brief note I observe
that the dual complex is a flag complex; that is, a collection of irreducible
boundary divisors has nonempty intersection if and only if the pairwise
intersections are nonempty. Rather than proving this directly, I translate the
statement to a setting in phylogenetics where it is widely used and multiple
explicit proofs have been written. It appears this result is known by experts
but lacks a detailed reference in the literature, except recently for $n=7$.
