  In this short note, we answer a question of Martin and Sanders [Integr. Equ.
Oper. Theory, 85 (2) (2016), 191-220] by showing the existence of disjoint
frequently hypercyclic operators which fail to be disjoint weakly mixing and,
therefore, fail to satisfy the Disjoint Hypercyclicity Criterion. We also show
that given an operator $T$ such that $T \oplus T$ is frequently hypercyclic,
the set of operators $S$ such that $T, S$ are disjoint frequently hypercyclic
but fail to satisfy the Disjoint Hypercyclicity Criterion is SOT dense in the
algebra of bounded linear operators.
