I believe it's possible to set up some instant messengers to IM you when you're not online, via sms. That would count toward your usage, but that's a step you'd have to intentionally take.
ATT is giving people confusing advice because AIM when used through almost all other phones uses sms for the service. The iPhone uses it's own app which sends the info on a data network, completely independent of the typical phone company's sms [scams].
It's equivalent to using AIM on your desktop, or more specifically, AIM usage on the iPhone falls into the same category as browsing on mobile Safari.