The simple plug-in testers with three lights cannot detect every possible problem. They just have the three lights wired across each possible combination of hot, neutral, and ground. i.e. H-N, H-G, N-G. At a correctly wired receptacle both neutral and ground will be at (or very near to) ground potential, leaving the H-N and H-G lights illuminated. Connecting the receptacle ground to the neutral results in the same voltages at the outlet, so the tester indicates "All O.K." You'll notice that the guide to the light combinations on these testers has "Hot-Neutral reversed" and "Hot-ground reversed," but no "Neutral-Ground reversed." That's because they can't detect such an error.
The case of the appliance wouldn't have been energized so long as all connections remained sound. If the neutral ever opened somewhere along the circuit however, then the ground pin on the receptacle would rise to 120V taking the casing with it.
Far too much reliance is placed on these cheap testers.