No such business does this.

Businesses that do white / private label goods often don't want to say who the original manufacturer is. For example, my daughter has a Cyberpower PC gaming laptop and it took some digging, but we found the original Chinese manufacturer and from there were able to track down drivers and other things.

"Such business." A local deli, on the rare possibility that they sell their own white-labeled baked good, would probably tell you where it came from anyway. The fig bar in question was not a white labeled or private label good anyway. But if you asked the guy where the greek salad, potato salad and pasta salad come from he would tell you.

A retailer is also different than a direct seller/manufacturer (your example).