Until yesterday I thought that it was not possible to send background SMS without using the IOS SMS interface (Which many people here assure also). However, today I downloaded a
Having tried the app, I can verify that it does send SMS programmatically, without showing the SMS interface. And it clearly doesn't happen through a third-party service, since the message gets sent as an iMessage when possible.
It's also clear from all the other answers that there aren't any public APIs for sending SMS programmatically, so the developer must have used a private API and yet somehow snuck this app through the approval process.
Specifically, it seems he used the CoreTelephony API. This post on SO describes the procedure. Apparently you'll also need to get your hands on the CoreTelephony header files somewhere.