Some of the earlier BE versions did not correctly work with authenticated SMTP after there was a small change (in the e-mail applications, not BE) in the way Authenticated SMTP worked. As such if you are on BE 12 (and not 2012) and your google mail setup requires authentication then that is likely to be the cause.
Solution to this would be either use a newer version of BE, or setup an internal mail relay that can accept unauthenticated SMTP from the media server (lock it to IP address if you have security concerns) and then relay it onto google mail with authentication.
You will need some kind of 3rd party application to do this and no I cannot recommend one.
