Extremality under direct sums

Prove that the direct sum of extremal matroids is extremal: if matroids M_1,...,M_s are extremal vertices of the corresponding polytopes, then M_1oplus3 M_s is extremal.

Background

The paper defines a matroid M to be extremal when its point p_[M] is a vertex of the unlabelled polytope Omega_{r,n}. It proves one direction: if a direct sum is extremal, then every direct summand is extremal. The converse would characterize extremality for disconnected matroids in terms of the extremality of their connected components. The authors report computational verification for disconnected matroids on at most seven elements, but leave the general assertion unresolved.