Fidelity (aka: Truth or Consequences) - S1-E7
Trivia: On the TV after House finishes watching his soap, its credits are rolling. Most are made-up names but two are in-joke references to staff members. Marcy Kaplan as Hair Stylist - usually credited as Marcy G. Kaplan, she was an Associate Producer for that episode and is now a Co-Producer. And Cindy Carr as Wardrobe - she was a Set Decorator for the entire first season except for the Pilot.
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