Google has feature that let developers to use Google Account credentials and login. All the login information will be processed on Google servers and third-parties couldn't get access to your credentials. (It's like Facebook/Twitter Connect)
I prefer to use such a way to login to my Google Voice, instead of giving OBI my credentials.
I know that this post is nearly a year old! ::)
But I fully agree, and hope that perhaps more comments will be made on this, and seen by OBIhai.
The Google Connect API would seem to be the more secure method to authenticate.
To avoid giving your gmail password, you can use Google account 2-step verification and generate an application specific password.
I use 2 step myself. If you really don't want to give up your password you can also set up the obi directly like I did via it's local ip.