I would think it has to be in the line or in the faucet. If the mold is floating on your beer after a pour, it would be very tough for it to be sucked from the bottom of the keg, where the dip tube pulls from. typically, mold would float on any surface, so doubtful it was growing on the bottom of the keg.
I always take apart the faucet and clean it in between beers, as well as run some cleaner through the lines.
also, when I know I'm done drinking for the night, I spray some water in the faucet and clean that out with a brush, then hit it with a quick spray of starsan solution inside.
Either way, it seems odd, I've owned the kegerator for almost 15 years and never had an issue with any mold in my beer.