Merry Little Christmas - S3-E10
Other mistake: Just by looking at Abigail's mother, it is obvious that she does not have cartilage hair hypoplasia (Meredith Eaton has pseudoachondroplasia).
Other mistake: House and Wilson are in the Mens room, and there is a tampon/sanitary pad dispenser. (00:21:30)
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