Every US airline (121/135) operates under a Minimum Equipment List (MEL). These MELs and their cousin NEFs (Non-essential Equipment and Furnishings) allow the airline to operate aircraft with certain specific equipment inoperative. Through these FAA certified programs once an item is discovered broken and that item is listed accordingly then it can be deferred per the MEL/NEF for a specific length of time. Each deferment requires a signature and usually some type of remedial action like the voice announcement in your example. These deferment programs are highly regulated and used in all areas of the aviation industry.