The non-optimal edge-coloring equivalence conjecture

Let $G$ be a graph, and call an edge-coloring optimal if it uses the minimum possible number of colors. Two edge-colorings are equivalent if one can be transformed into the other by a sequence of Kempe swaps; a coloring is non-optimal if it is not optimal.

The non-optimal edge-coloring equivalence conjecture. Any two non-optimal colorings are equivalent.

This is presented as a consequence of the stronger question asking whether every optimal coloring is equivalent to every given coloring. The supplied source does not state whether the conjecture is resolved.