Haha, definitely not. The BBB is a joke, and fundamentally dishonest. They pose as a quasi government agency, and people who don't know any better believe them. The use of the term "bureau" is entirely misleading. They're a completely for-profit operation running a credibility scam as far as I'm concerned. "Pay us to become credible!".
Its not too unlike those ridiculous companies that offer contractors "best of the industry awards" for the low low price of 1000 dollars.
No one that I'd like to give any money too. I would be embarrassed to have their logo on my website or business card.
Home Advisor is similar. So many atrocious companies like them that act as lead generation services, mostly ripping off unsuspecting young business owners who believe the lies they tell you about how many leads you'll get through the service. Meanwhile they position themselves perfectly with SEO so Home Advisor, Yelp, etc. are ranked first in Google and other engines, funneling leads through their pay-to-play business model and beating out real company websites in organic searches.