In Person of Interest Season 2 Episode 16 "Relevance", Hersh grabs Shaw from behind and injects her with poison and she collapses. Later, Carter and Fusco tell the officer on the scene that it was an overdose and tell him to get some coffee. The officer leaves and they tell Leon, posing as an EMT, to haul the body away.
Later, Shaw wakes up in and ambulance and finds Reese and Finch and says that they showed up late. For which Finch points out that they wanted her to be believed as dead.
However, how do they know that Hersh is going to poison her when the goverment could have ordered her shot by someone else. Hersh is also shown to kill people by methods other than poison? He could have strangled or shot her.
Even for poison, how were they sure that they have enough time, Hersh might have given some quick poison.