The Better Business Bureau takes complaints from customers that have had a problem with the business; i.e., not getting what they ordered, getting defective goods. Then they send a copy of the complaint to the business that can refute or whatever. As long as the business answers and explains their side of it, they are pretty much in good stead with the Bureau. The Bureau is structured to be serve businesses because they are the ones that pay dues to belong, which financially supports the organization.
Checking with the BBB could tell you if the breeder had done something such as taken a deposit and not delivered the dog as promised, etc. It would not help concerning the quality of the puppy. Lots of back-yard breeders probably aren't even licensed businesses, in which case the Bureau probably wouldn't represent them anyway.