In my humble opinion, the main benefits of a BBB accreditation are not SEO authority, but:
- Using the accreditation seal in print and banners to generate trust,
- Add the company's BBB-page as a review extension in Google AdWords - one of the few extensions that is generally accepted by Google as a valid reference.
This will not help with SEO ranking, but will improve the conversion rate, clickrate in AdWords, and therefore AdWords Quality Score and PPC ranking.