Other mistake: Amber states that Chase has a cat, even though in several other episodes Chase says he doesn't have a cat and wouldn't let Cameron get one because he hates cats. (00:16:10)
Continuity mistake: During the scene in which House is offering up liquor-flavored ice cream he sets the containers in a row down the table 1-2-3-4-5. He then puts spoons in the three containers closet to Foreman, 1-2-3. The shot changes and before anyone touches the spoons they are now in containers 1, 2, and 4.
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