I think Xemnas told Roxas and the others outright lies.
Nobodies are "No bodies."
Heartless are "heart-less."
Nobodies aren't nobodies because they don't exist, as is often the common interpretation. They are nobodies because they are without bodies.
Heartless are beings without hearts but with a body.
Nobodies don't have hearts. They ARE hearts. This is also why Roxas, Axel, and the others can use their weapons.
They have feelings and emotions, and some memories. Xemnas told them this, to use them. To convince them there was a need to gather hearts for him. But they already are hearts, they just don't have a clear connection to their original body. They never needed to create Kingdom Hearts, but they were told that they would give them "hearts of their own" as Axel said.
