Oh - if anyone is still curious: I recorded the greeting via the phones custom greeting function, then called to listen to it from another phone, then turned off the phone and called again. Same message. I had wondered if just maybe the phone played the message when on, and the carrier played the message when the phone was unreachable.
When recording, choose a quiet area, speak clearly, and use your full name (first and last).

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You can record the greeting on your own, and maybe leave a cute message for your sweetheart or a more professional greeting for work associates. You can also type in messages that will be dictated by one of eight different voices. There are three French voices, three English voices, and two Spanish voices, and it actually ended up being a much funnier experience than I thought it would. If you get creative enough, the different automated voices can be pretty hilarious, and greetings are sure to get an interesting response from your friends.