I have one gmail account configured to access another gmail account.
Now, here comes the fun part - how to fix it.
I logged with the other account (the one google claims is hacked) and I got a message similar to this one:
And then I have to click Yes:
And then I have to log in quickly.
Weird. Google migrated to this security protocol without notifying me. I have this new application style log in on my primary account, but not on the "cracked" one.