When the agents first appear while some cops are dying inside the Hearth O' The City Hotel at the hands of Trinity, whose body do they posess?
Except this scene, most of the time they consider the situation so bad that they outright possess a nearby body. In this case, however, they come by car. Do they have a dummy body for everyday situations?
Continuing to possess the last human they used would be risky because people would keep disappearing.