Outlet tester says "Correct", but there is no ground wire
Assuming you are in north america: In a home wired up with armored cable, otherwise known as BX or AC cable, the armor is the grounding conductor. It is always terminated to a metal box with a cable clamp that secures the cable and completes the connection between the box and armor. The metal mounting bracket(called the yolk), which is the frame of an outlet, is not only mechanical but also serves as a ground conductor for the outlets ground prong(s), the grounding terminal screw and the cover screw. The ground connection is made in one of two ways: via the ground screw or the mounting screws which secure the yolk to the box. The yolk method is acceptable in armored cable systems.

Newer MC or metal clad cable looks exactly like armored cable but has its own grounding conductor. In that wiring system, the armor is not listed for grounding and the wiring methods are similar to that of terminating non metallic cable (aka romex). Meaning, the ground wire must be connected to the metal box, the outlet, and any other grounding conductor.