I'm reading Ghrist's paper "Configuration spaces and braid groups on graphs in robotics". In this discussion, counterexamples are shown for both Theorem 2.3 and the implication "Theorem 2.3 $\Rightarrow$ Corollary 2.4". Are there other proofs, in literature, that configuration spaces of trees are Eilenberg-MacLane spaces? Or, is there a way to "fix" Ghrist's proof?