I was attempting to upgrade an old outlet to a GFCI outlet. There are only two wires one black and one white. There is no ground wire. However the receptacle tester read "correct wiring". Is it possible that the outlet is grounded in some other fashion?
When you say the receptacle tester read "correct wiring", I am assuming that the existing receptacle was a three prong (had a ground pin) and that the tester was also a three prong, something like this.
If that is the case, it is probably reading ground through the metal box and the armored cable.
Before plastic boxes and non-metallic cable that used a continuous run of a separate bare or green ground wire, there was a grounding system that used the metal strap of the receptacle or switch, firmly screwed to the metal box, firmly screwed to the armored cable with was also firmly screwed to the service panel and through that, to ground. In later years, a bare aluminum wire was also included with the hot and neutral which (I believe) was intended to be a bonding strip.
This system worked. Sort of. It assumed that the metal connections were direct and firm at each juncture. The weakest part was probably the strap of the receptacle, which often sat on plaster and never touched the box. No metal-to-metal connection, no ground (although the aluminum wire, if properly connected, would provide ground). The connectors holding the armored cable to the box were also sometimes loose, leading to poor connection and poor ground. I think it is still code compliant and may be fine if proper techniques are used to install it.