Locating a backtracking robber on a tree

Carraher, Choi, Delcourt, Erickson, and West (2012) [4] introduced the following version of a robber locating game: At each turn, the cop chooses a vertex of the graph to probe, and receives the distance from the probe to the robber. The cop wins if she can uniquely locate the robber after this probe. Otherwise the robber may stay put or move to any vertex adjacent to his location. We answer some of their conjectures and characterize the trees for which the cop wins.