My main concern would be the 'tape' you mentioned which may be insulating the bond of the AC armour and the box.
NEC 110.3 (b) "Failure to follow mfg instructions" (not verbatim NEC words) as the NM clamps are for NM, unless they are ID'd for AC, which some are.
Text from the 2011 NEC...
320.40 Boxes and Fittings. At all points where the armor
of AC cable terminates, a fitting shall be provided to protect wires from abrasion, unless the design of the outlet boxes or fittings is such as to afford equivalent protection, and, in addition, an insulating bushing or its equivalent protection shall be provided between the conductors and the armor. The connector or clamp by which the Type AC cable is fastened to boxes or cabinets shall be of such design that the insulating bushing or its equivalent will be visible for inspection. Where change is made from Type AC cable to other cable or raceway wiring methods, a box, fitting, or conduit body shall be installed at junction points as required in 300.15.
I based my previous comments on your description.