No. Bitmain is selling the pickaxes. Coinbase is the tent where the gold miners take their nuggets to sell.
Like it or not, it's a phrase that dates back to Mark Twain that has far more baggage than some strict analogy made up on the spot. For instance Chris Dixon here[1] suggests that Heroku and Akamai sell pickaxes, not dynamite as a service or scalable ore transport systems.
All I'm doing is defending the GP's use of the phrase, which was absolutely valid. Perhaps you'd have used a different analogy, but it doesn't invalidate his. No quantity of curt denials you care to throw my direction will change this.
[1] http://cdixon.org/2011/02/05/selling-pickaxes-during-a-gold-...