In the US an aircraft is not considered airworthy if something is broken unless it is an aircraft with an FAA approved MEL (Minimum Equipment List). In that case the MEL spells out what is actually needed for flight and any restrictions. For example you might be able to fly with prop heat inop if you are not flying into predicted icing conditions.
Not sure where your issue took place and I'm not familiar with rules outside the US. Plenty of FBO's here routinely rent aircraft that have broken equipment. If something occurs the pilot will be violated by the FAA for departing with inoperative equipment. So unless it's something trivial I'd use caution.