Regardless of whatever private insurance it has, Coinbase does not have a money transmission license in California or a surety bond as required by federal and state law.
They know they need one; they have applied in other states, such as Florida. See https://archive.org/download/coinbasefloridamtl/20140415.coi....
Interestingly, Coinbase appears to offer false information to the State of Florida in item 6(A)(2) of its application, which has since been withdrawn. Coinbase did receive a subpoena in the NY DFS's investigation of various Bitcoin companies in August, 2013. See http://www.reuters.com/article/2013/08/12/us-digitalcurrency....