The weak benignity conjecture for subsets of models of stable theories

Let $T$ be a stable theory, let $M$ be a model of $T$, and let $A\subseteq M$ be arbitrary. The set $A$ is weakly benign in $M$ if equality of strong types over $A$ implies equality of the corresponding types in the language expanded by a predicate for $A$. The weak benignity conjecture. Every arbitrary subset $A\subseteq M$ is weakly benign. The source presents this as a weakening after refuting the stronger benignity conjecture. No resolution of the weak benignity conjecture is given in the supplied text.