I used the option of linking my Wells Fargo bank account to coinbase with my Wells Fargo username and password because it seemed like the fastest way to get everything setup.
After the Wells Fargo authorization went through, I immediately changed my Wells Fargo password just in case coinbase was saving the Wells Fargo authorization in fear of what would happen if coinbase ever got hacked.
A couple of days later, I got an alert from Wells Fargo about my account being disabled from too many invalid login attempts.
This is not a coincidence. Whatever caused this would certainly be related to the fact that I signed up with coinbase. I never log into Wells Fargo and I did not attempt to login with other programs such as mobile apps etc.
I'm sorry if this seems overly alarmist. I have filed a support ticket with coinbase but I got a reply which simply said they are overwhelmed with support tickets and there's a long wait. I have also tweeted at them.
Interesting that the bitcoins were successfully purchased so I am confident that the link to withdraw money from my bank is set up correctly.
For now, I would strongly suggest avoiding that feature until further notice.
Screenshot:
http://screencast.com/t/4waKr2DD