No, it doesn't apply to the U.S. However, if you cross over to either Canada or Mexico, you will be charged the "overseas" rates, so be careful if you live close to those areas.
Actually this is only partially true, a convenient half-truth lie propagated by the marketing department at AT&T.
Many, many places in the US have no proper AT&T coverage.
In some of them, they have reciprocal agreements with other carriers. Although this is -- at first -- included in your monthly plan, this is not technically "on-network". If you travel extensively in such areas, you'll raise the ire of AT&T until they cut off your service. In other words, make sure that you don't rely on AT&T for anything mission critical. This is why I know carry a phone on another carrier.