Marilyn & Bob wrote:

The OP said that he lives in New York City where BX (armored cable) was
required in the 1920s (and still is today). Cloth covered wires with
armored sheathing is standard in older building in NYC. This is not knob
and tube. It is BX and it is grounded (although some may question whether
the armor provides an adequate ground.

Yep. Back in those days steel BX was intended to prevent vermin from
eating the wire insulation. A manufacturing flaw resulted in rusting
between the spirals of the armor. If used as an equipment grounding
conductor the impedence may very well be high enough that the fuse or
breaker won't trip upon a ground-fault, resulting in a possible fire as
the armor heats up. IMO, the OP would be better off installing a 2
wire receptacle or a GFCI receptacle.