I've always had my reservations about that:
...The Omani Arabs posed the most direct challenge to Portuguese influence in East Africa and besieged Portuguese fortresses, openly attacked naval vessels and expelled the remaining Portuguese from the Kenyan and Tanzanian coasts by 1730. By this time the Portuguese Empire had already lost its interest on the spice trade sea route because of the decreasing profitability of that business. Portuguese-ruled territories, ports and settlements remained active to the south, in Mozambique, until 1975.
Omani Arab colonization of the Kenyan and Tanzanian coasts brought the once independent city-states under closer foreign scrutiny and domination than was experienced during the Portuguese period. Like their predecessors, the Omani Arabs were primarily able only to control the coastal areas, not the interior. However, the creation of clove plantations, intensification of the slave trade and relocation of the Omani capital to Zanzibar in 1839 by Seyyid Said had the effect of consolidating the Omani power in the region.
Omani Arab
Photographed in Zanzibar, 1890
Perhaps by choosing to portray Obama Snr as 'father' another can of worms was opened...for later?
Maybe Lamb was confused when people talk about Afro-Arabs, perhaps thinking that is a racial term. African-Arabs or Afro-Arabs are Arabized Africans. Racially, they are African but culturally they are Arab.