For the benefit of anyone following this thread who's not familiar with the jargon, or with the conflict between casual talk and strict NEC usage...
Article 320 AC cable, introduced around 1959, includes a bonding wire, aka drain wire, so that its metal jacket is listed and NEC-acceptable for use as an Equipment Grounding Conductor.
The 80-90 year old BX we're discussing, like modern Article 330 MC, has a jacket that is no longer an acceptable EGC.
Casually, "AC" might be used to include old BX, or to MC. And some folk use "BX" to refer to modern AC or MC. But for NEC, or GEC, purposes, they are quite distinct.
Historian Al, how'd I do?