The flaw in that little theory is that it is well known to both scholars of Islam as well as of Spanish history that those "Moors" 1- did not "occupy" anything in the Iberian Peninsula for "800 years" (not even Granada) & 2- were also nothing but a small elitist foreign minority, the key to the long survival of Islam in some parts of Iberia being obviously due to mass conversions of native peoples to the Islamic faith:
"What deep roots Islam had struck in the hearts of the Spanish people may be judged from the fact that when the last remnant of the Moriscoes was expelled from Spain in 1610, these unfortunate people still clung to the faith of their fathers, although for more than a century they had been forced to outwardly conform to the Christian religion, and in spite of the emigrations that had taken place since the fall of Granada, nearly 500,000 are said to have been expelled at that time. Whole towns and villages were deserted and the houses fell into ruins, there being no one to rebuild them. These Moriscoes were probably all
descendants of the original inhabitants of the country, with little or no admixture of Arab blood; the reasons that may be adduced in support of this statement are too lengthy to be given here; one point only in the evidence may be mentioned, derived from a letter written in 1311, in which it is stated that
of the 200,000 Muhammadans then living in the city of Granada, not more than 500 were of Arab descent, all the rest being descendants of converted Spaniards."
http://archive.org/stream/preachingofislam00arno#page/144/mode/2up
So the Arabs/Moors of southern Spain would have had even less of an impact than any Roman or Vandal invaders from previous centuries. Like all military invasions, they simply weren't there in large numbers. In fact, it would be expected that Italy itself would have been more affected by the well-known large number of immigrants and slaves imported to the Italian peninsula from all over the empire, particularly from the Eastern Mediterranean regions, like Greece, southern Balkans, Anatolia/Turkey and the Levant.