What is the difference between symmetric bipartite graphs and a complete bipartite graph?
Your first link's usage of 'symmetrical bipartite graph' is indeed puzzling. From my knowledge of RBMs it would have been better for them to say 'complete bipartite graph' as you suggest.

The only formal reference I can find online for 'symmetry' in bipartite graphs is this link. But that does little to explain the usage in your case.