Were The Nabateans Ancient Jordanians?

This I found at the official Jordan Petra News Agency site and piqued my interest:

The Nabateans, an Arab people, were among the first to settle in Jordan, with their base in Petra.

As a country called Jordan did not really exist at that time. Even Wikipedia knows that 

Jordan refers to the history of the Hashemite Kingdom of Jordan and...of the region of Transjordan.

Note the description here, for example:

Among the oldest references to Arabs in what is now Jordan is the account of the battle of Qarqar in 853 BCE,

And here:

Nabataeans...carved into the rose-red rocks of present day Jordan 

a source which also illuminates that they were not that native:

The Nabataeans probably originated as a nomadic Arabic tribe known as the Nabatu. They emerged in the seventh and sixth centuries BC, migrating into the region which today forms parts of Jordan... 

The Britannica only mentions Jordan as a river:

Nabataean, member of a people of ancient Arabia whose settlements lay in the borderlands between Syria and Arabia...When the Roman emperor Trajan annexed the kingdom (AD 105–106) and set up the new province of Arabia, Bostra (Bozrah), east of the Jordan River, was chosen in place of Petra as the provincial capital.

The Nabateans were not ancient Jordanians.

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