Both of you are right given certain circumstances. if you think in terms of potential deference instead of simple continuity and resistance and the type of instrument you choose to test with. Given a simple circuit and known factors like good power supply and Good return to ground a continuity test with fuse in place should be a good and valid test.That being said modern electronics have many circuits that may be above ground potential and rely on potential differences between voltages such as holding a state of I/O in a computer signal. In this situation a beep or even test light has the potential to give a false signal related to ground. A voltage meter is the best tool to use because it will show the potential difference no matter what. The days of simple circuits is well over with in regards to electronics and even a miss placed test lead can cause catastrophic damage to a computerized control circuit.