If it’s a lie, it’s an old one, in that the Arabs have been called variations of “Ishmaelite” way before the false prophet Mohammed came along.
Only because anyone who had no heritage wanted one so they took Ishmael’s. So that made them feel as important as the Jews who had a lineage and history they could point to.
However even at that the followers of Muhammad eventually had to write a genealogy to prove he was a descendant of Ishmael, so they invented layers to get connected to a guy who’s descendants never got within 1000 miles of Mecca.
Once they connected themselves to Ishmael, they then can claim they are following the One true Gos, but they are not. They are following Muhammad’s god who is the moon god.