Well, to be honest, Texas doesn't have this accent - alone. Pretty much, people in Oklahoma, Arkansas,and much of the mid-south (Appalachia, where I'm from) also have this accent. In fact, the whole southeast US has this accent - to some degree, though, it's disappearing as people from other areas are moving in.
Anyhow, the article was saying Texas had a particular "take" on the southern accent. However, what I've heard of W. Bush - sounds just like someone from East Tennessee, where I'm from - as in exactly like it! Well, does anyone feel different? Why might you be right?