That's only 22 generations to span 1300 years. That's not very plausible: the average age of each father when they had the relevant child was sixty.
Not quite as absurd as the Methuselah lineage, but still extremely hard to believe.
I don't think your moral point is dependent on this either way--if the Husseini family was in the area since 700CE that's plenty to establish historical ties (heck, since 1700CE would be plenty).
Are you trying to signal to other Muslims that you're one of them without coming out and saying so point blank?