A set of vertices S ⊆ V (G) is a basis or resolving set of a graph G if for each x, y ∈ V (G) there is a vertex u ∈ S such that d(x, u) = d(y, u). A basis S is a fault-tolerant basis if S \ {x} is a basis for every x ∈ S. The fault-tolerant metric dimension (FTMD) β ′ (G) of G is the minimum cardinality of a fault-tolerant basis. It is shown that each twin vertex of G belongs to every fault-tolerant basis of G. As a consequence, β ′ (G) = n(G) iff each vertex of G is a twin vertex, which corrects a wrong characterization of graphs G with β ′ (G) = n(G) from [Mathematics 7(1) (2019) 78]. This FTMD problem is reinvestigated for Butterfly networks, Benes networks, and silicate networks. This extends partial results from [IEEE Access 8 (2020) 145435-145445], and at the same time, disproves related conjectures from the same paper.