While you are focused on whether I correctly used quotes, "covert," or "clandestine" I was amused by the irony in trying to maintain the appearance of any of these in the face of the obvious fact that the cover had been blown.
It's done because sometimes 'the obvious' isn't so obvious to everyone else. The intentional uncertaintly and confusion around an already confused event may very well save lives and/or time. Certainly the alternative, running to a soapbox and announcing to your enemies that your personnel are spies and have 'obviously' crashed in enemy territory, is not a good idea.