Illustrating an error in "An equivalent condition for a uniform space to be coverable"

Berestovskii and Plaut introduced the concept of a coverable space when developing their theory of generalized universal covering maps for uniform spaces. If a space is coverable and chain connected then it has a generalized universal covering map. Brodskiy, Dydak, LaBuz, and Mitra introduced the concept of a uniformly joinable space when developing a theory of generalized uniform covering maps. It is easy to see that a chain connected coverable space is uniformly joinable. This paper discusses the attempt in Plaut's "An equivalent condition for a uniform space to be coverable" to prove that a uniformly joinable chain connected space is coverable.