Factual error: House is playing 'Metroid: Zero Mission' on his Gameboy at various times. The Metroid series does not feature space monkeys, nor are there distinct levels. The sounds coming from the game in the show do not match it in real life, and Samus morphing into a ball is most definitely not a failure state.
Factual error: The whole episode is caused by medications being mistaken for one another. But the reason why is actually impossible. The patient states that the pills he took (in error due to a switch) had no letter or marking on them. With few exceptions - none of which apply to the medication the patient took - the US FDA law states that all solid medications must have a letter and/or number on each pill which allows them to be identified. No pharmacist would ever give out blank pills.
Answer: She would have No Reason to know it belonged to the CIA. If she did know he went off in the helicopter, all she would know is that it wasn't an ambulance helicopter.
Greg Dwyer