My comment was based on this part of your post. I misread that they tested the alternator. As I pointed out, driving the car with a voltmeter attached can reveal many hidden defects.
If there is a major slippage of the belt there will be a)audible signs, b)vissible signs on the belt and pulley and c)smelly and smoky signs.
Modern car is a system, not a sum of many parts and control modules. It cannot be properly diagnosed if one is looking only at the part that fails to function.