Full Euclidean Steiner tree degeneracy conjecture for minimum Steiner point trees

Let $N$ be a set of terminals embedded in the Euclidean plane, and let $T_S$ be a full Steiner minimum tree on $N$. Full-tree degeneracy conjecture. There exists a minimum Steiner point tree on $N$ that is a degeneracy of $T_S$. The claim would support improving Steiner-tree heuristics through Steiner-point displacements, but the supplied text gives no resolution.