Grounded Armored Cable?

Hello-
My house is over 70 years old. Wired with armored (BX) cable - cloth wrapped hot & neutral inside. No ground wire.

I've been gradually replacing ancient receptacles with 3-prong ones. I've been pigtailing the ground screw to the metal outlet boxes. I've been testing each box with with a voltage tester (one of those little ones that's just a small light), and I've since acquired one with a digital readout for the last few. Indeed, I'm seeing the same voltage (~124v) from hot to neutral as hot to ground - indicating (i think) that the boxes, via the armored cable, are grounded.
However, I've recently read some postings claiming that armored cable doesn't provide true ground - that there is so much conductive material joined by the boxes and all of the cable sheathing that current will flow into it, but that there still may be a more direct path to ground in the event of a short circuit.

so, is that true?

I have no way to measure the current, only the voltage. Do I have a grounded system?

This is very true.

The problem is not that of finding a different path, it's one that a fault will follow the spiral of the sheathing and not run along it in a linear path. This creates very high resistance and can cause the sheathing to be a heating element instead of a fault current conductor.

Modern AC cable (~1960's on) has a thin bonding strip that "joins" all the spiral coils and lats fault current flow directly down the cable.

Speedy Petey answer was very good. I would just add, If the amored cable is not a good grounding conductor, install GFCI duplex receptacles. This is an opinion on mine. Replacing the old BX cable is better, if you have the funds to do this.??