No, but it's there as a baseline.

So in the original scenario above, either:

• the AI's lying about its capabilities, but has determined regardless that the threat has the best chance of making you release it
• the AI's lying about its capabilities, but has determined regardless that the threat will make you release it
• the AI's not lying about its capabilities, and has determined that the threat will make you release it

Of course, if it's failed to convince you before, then unless its capabilities have since improved, it's unlikely that it's telling the truth.