Vmca (Minimum Control Speed in the Air) is unaffected by bank, or anything else come to that, it is an absolute figure for each aircraft and can be found in the Flight Manual/POH/etc. It is defined in BCARs as:
The minimum speed at which, if sudden and complete failure of the critical power unit occurs during the take-off climb out, it is possible to regain control and thereafter maintain straight, steady flight at the same speed. The change of heading should not exceed 20 degrees and the final angle of bank should not exceed 5 degrees.
What the officer meant to say was that Critical Speed is decreased if bank is applied towards the live engine. It is theoretically possible to overcome all asymmetric forces if sufficient bank is applied, removing the need for any rudder. However, this technique would cause more problems than it would solve and the generally accepted angle of bank to be applied is 5 degrees.
The problem is that the aircraft is not easy to fly accurately at 5 degrees angle of bank without constant reference to the AI, and one certainly does not want to be glued to the instruments at this critical stage of flight. Neither is it easy to keep in balance, since the slip indicator will not be central and balance will have to be judged by reference to yaw in relation to an external visual reference or the turn co-ordinator/compass. For these reasons, it is recommended that, where performance is not critical, the aircraft is flown wings level with the slip indicator central.
The pilot who understands the problem will be capable of adjusting his handling of the aircraft in response to the conditions pertaining at the time, he/she may need bank towards the live engine, he/she may not. With the greatest respect to the FAA and Mr. King, to say that flying "wings level with the ball in the middle is NEVER correct" is something of a cop-out and avoids the pilot having to think for him/herself. It would be more accurate to say that flying with 5 degrees of bank to the live engine and the aircraft not yawing is never wrong.
The measure of a good pilot is one who can think for him/herself and make valid decisions based on a thorough understanding of the principles involved, not simply reacting in a fixed way only because the King video said so.
Nobody will fail a JAA skill test for flying an asymmetric aircraft wings level with the ball in the centre (if performance is not a consideration). However if, in making an unnecessary attempt to fly with 5 degrees of bank to the live, he/she allows the aircraft to drift off the required heading, a fail will surely result.