I recently turned on two-step verification for my Google account and installed the Google Authenticator app on my Android device. Based on what I have read everywhere (even Google's official info: http://support.google.com/mail/bin/answer.py?hl=en&answer=1173270), I was under the expectation that I would have to generate an application specific password for some of the apps on my Android device - gmail, youtube, etc. However, that hasn't happened. Everything continues to work fine on my device including gmail, youtube, sync functionality, etc. I have restarted the device, forced it to sync manually, etc...no problems, and I'm never prompted to enter a verification code, never set the device as trusted, etc.
How does this work? Are the Google Android native apps using the Google Authenticator service behind the scenes to generate codes?