"Unless there is some kind of short (which will blow a fuse) or other fault in the bulb itself (i.e. one that keeps the light circuit open without passing current through the filament), it is hard to see how they could cause general electrical problems. "
The issue isn't the luminance nor the color of the light - it is the electrical consumption of the aftermarket lamp compared to the original. The alternator is usually sized for the electrical demand of the stock vehicle, under average driving conditions. Night lighting is one of the most demanding states for an alternator to cope with. Double the lighting current consumption, and sit idling in rush hour traffic every night, and the conclusion of the dealership is very reasonable. There are other possible causes, but as Haasman pointed out, an easy diagnostic would be to replace the lamps with the originals and see if the electrical system now comes up to par.