[AStonesThrow]

The only preposterous idea in this scenario is that anyone assumed the LLM would keep a secret to begin with.

Well okay there's another preposterous idea: that the LLM could know the truth about the affair in the first place.

So they told this LLM, through prompts, that an affair existed. Liars. The LLM could also infer, through user behavior, that something was going on. Hallucinator.

Since an LLM has no concept of truth or means of fact-checking anything, the solution here is simply to pre-load your context with bullshit and hallucinations, and any blackmail attempt will be filed under "Boy Who Cried Wolf".