I certainly can't see any benefit in making life more difficult than it already is. (not that it is a difficult situation...yet) There are no immediate actions from the QRH wrt B737. I would be surprised if there was anything in any other type.
If the aircraft is otherwise serviceable, then I think the best response is to continue, but have a good review of what's going on, and what you might do if other problems present themselves.
If the aircraft is carrying associated defects, such as pressurisation systems having a history of problems, then this would maybe focus attention on other immediate actions.
In the scenario given, it can hardly be expected that the interviewee would have a well considered response without in-depth knowledge of operations.
From an airline questions point of view, I would be interested in how the discussion went on.
I'm inclined to say that point of the question is to see how you incorporate new ideas and information to develop your response.