Correct. Many Hashemites trace their lineage through Muhammad’s Uncles such as Abbas who created the Abbasid Caliphate.
Which is why having people like the King of Jordan being friendly to the West helpful, since is a descendant of the Prophet, unlike the backstabbing Saudis.
Mind you, back then there was no distinction between what we over the last century call Jordan and Saudi Arabia; it was one 'country' ie Arabistan, with factions or clans of the same tribe fighting one another. Although, I do have much respect for present-day King of Jordan, and he isn't comparable to the Saudis.
But not for the Umayyads or the Abbasids, historically speaking. The Abbasid were just more wily in their approach to Islamization of non-Islamic lands such as Iran. They tried their utmost to combine local traditions & culture with their bedouin Arab Islam. Later, put an Islamic spin on non-Islamic traditions (in a way similar to current Iranian regime) to have them accepted by the newly converted to Islam locals and other non-muslims.
Anyhow, I think one of the 'four countries', not mentioned in the originally posted article, which ISIS says it intends to go after is Jordan.
P.S. - a former president of the Mullah regime in Iran, who is a multi-billionaire, and known to be a wheeler and dealer too, over & above the political scene, has a lastname of “Heshemi-Rafsanjani” ;)