I wrote this circa 2014. Since then, a lot of things have changed, and a lot have stayed the same in the Bitcoin community. I forgot to publish this, but am doing so now to reflect on changes.
Yes, Coinbase can send Bitcoins from your wallet without your permission.
Last week, Coinbase announced a promotion where new Coinbase accounts registered with a .edu address would receive $10 worth of Bitcoins for free.
My friend John (named as so for the purpose of this post) and I realized that not everyone we knew were going to be interested with Bitcoin. We came up offering $5 upfront for the Bitcoins each person received if they signed up for a Coinbase account.
John was able to get 18 interested individuals in sending him their account balances, coming up to a total of .47005 Bitcoins. I however had a less impressive amount.
Later, John received an email notification from Coinbase that someone had emptied his wallet balance.
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That someone was Coinbase. Make no mistake that Coinbase in all intents and purposes is not a traditional wallet. They will "spend" your coins if it suits their interests, as is seen here.
Keep all of this in mind when we head towards increased adoption of Bitcoin.