It is not a lie. The message is stored in their SMS-C exactly until it has been delivered to the recipient. Then it is discarded.Once I got a text message from someone 24 hours after they sent it. So for 24 hours that data was living in AT&T's computers.
So they say it's not saved at all and I say it can stay on their servers at least a day, apparently. So now that we know the statement isn't true who's to say where the truth really lies? 2 days? 3? A week? A month?
No way to know, unfortunately, since we know that what they're telling you is a lie.