I have heard that if a meter needle is centered in a permanently positioned scale AND its meter needle stays centered when power is off, it uses a Wheatstone bridge circuit and is not subject to devialtions caused by different voltage (alkaline cell).
That is correct. If the needle position for correct exposure is the same as the position the needle rests in with the power off and that position is the centre then it is a bridge circuit. As this circuit shows correct exposure when both sides of the meter are at the same voltage i.e. zero voltage difference across the meter then the actual voltage of the cell cannot alter this.