CEC 12-610 (1) ".....bushings of insulating material or equivalent devices." But consider subrule (3) which requires the protection to be visible for inspection when cable is installed in connector or clamp. So as long as the electrical tape is installed with that in mind it should be okay. Anti-shorts are preferred because they are quicker, easy to see and more reliable.
Tape vs anti short? I would not permit electrical tape to replace an anti short. Tape is too susceptible to cutting by the armour of the BX and it cannot be placed in between the armour and the wire either. In fact the insulation of the wire is already more resistant to cutting than tape itself. So what use is tape in this application?
My intent with referencing section 12 was just to say there is no specific reference to "anti-shorts" but it does reference insulating material or equivalent, leaving room for interpretation.
I have torn anti shorts while installing on bx, and I have always been able to wind back the armour enough that I could get several layers of tape on if needed. But I know that you are with inspections, so your post carries some weight.
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.
Looks like we are basically on the same page on this.