Wilber's 1st bound has a natural topological interpretation. View the tree as a geodesic metric space, and observe that the left and right subtrees (geometrically interpreted to include the nodes and all of their incident internal edges) of the y's in P define a laminar family of simply-connected sets, where each left-right pair is connected by a single edge in P.
Define two simply connected sets in the tree to be neighbors, if they overlap or are at distans at most one edge from each other.
Use such single-edge connectedness to define an neighbor relationship on the sets. Observe that each tree rotation is a "continuous transformation" which does not violate neighbor relationships among sets in the family.
More precisely, if two sets are neighbors, after a "continuous transformation" they
Therefore, by a topological argument it follows that accessing two elements from disjoint sets of the family requires crossing their topological boundary.