Let's clarify the area that we call The Delta. I'm a geologist who has spent years mapping and dealing with water and topographic issues in that area so I'm claiming authority on this point.   On the map Offer linked, the boundary of the Delta is in fact the green line. On the right the line exactly follows the low 'bluffline' which is the edge of the flat alluvial plain. And of course on the left, the boundary is the Mississippi River.   

The citation text on that map has used unfortunate and incorrect wording 'the land between the Mississippi and Yazoo Rivers', this is not correct. Other smaller subbasins are included and the boundary of the Delta is not the Yazoo but the bluffline.

So Memphis is right at the north tip of the Delta plain, though most of town sits up above the bluffline. Same deal with Vicksburg, it is a bluff town which overlooks the point where the Mississippi, the Yazoo, and the bluffline converge to form the southern 'point' of the Delta.   As the author said, the Delta begins in the lobby of the Peabody Hotel in Memphis and ends on Catfish Row in Vicksburg.