Issuing demarches is not nearly as grave a reaction as you seem to think. Most likely, the government insisted, without showing the original remarks of the embassy, that the ideas expressed by the Americans constitute interference, or evidence of interference, or intention of interference in Pakistan's political process. Most likely, the military conceded to the government's interpretation deciding that the concession was a small one and not worth challenging the government. Moreover, once the prime minister has claimed foreign interfernce publicly, not showing any reaction would have been construed, both nationally and internationally, as weakness.
Pakistan Army gave no seal of approval to the lie. That is your interpretation ‐ and a flawed one. The institution itself has not reacted. They did talk to the Reuters, unofficially. Guess what they said?