| "... who thinks a pre-buy home inspection should've caught this? Seriously, you could spot this just by removing the cover of the main/sub panel (or upstream j-box) where this "BX" branch originated." Asking a general home inspector to remove the cover frm every j-box and check wiring is well outside the scope of a normal inspection. They manage to not understand what they are looking at in main panels, let alone other places. The armor of BX (and AC and MC) are grounding conductors, so anything hooked to a hot and the armor should work. You are NOT allowed to use a grounding conductor to carry regular circuit currents. There may be nothing wrong with the wiring, since I doubt the OP tried hooking the light up correctly. Many things measure as "hot" (especially in old wiring) if a digital meter is used. Connecting a load from the hot to ground or neutral will often provide a path for the current leakage (and the bulb will not light). | 
