Since you are thinking of installations of BX you've seen in old dwellings, the history of local ordinance as applied by the electrical Authority Having Jurisdiction since the dwelling was built is what determines whether a particular run of BX is allowed to be used as a ground.
The current NEC is for new installations, as a general rule. The NEC will have bearing on modification of existing wiring in sometimes strange ways.
In my area, old BX (without drain wire) is grandfathered in as a grounding means if the BX is apparently installed to the codes that were in effect at the original time of install. I can replace a two wire receptacle with a grounded receptacle. . .if, and this is a big if, the box volume calculates.
Many, but not all, times it is something else that drives the total replacement of the BX.