The term "hispanic" never really was clear to me. Is a Black Cuban "Hispanic", since he's from Cuba and speaks Spanish? Or is he not because he's Black? Is a native south american "Hispanic" if he speaks spanish, even though he has no link with the conquistadores?
Anyways in Spain the arabic influence is indeed quite obvious, especially in Andalucia. It's not something they try to "hide" either, at least not to my knowledge. And later on you had Spanish rule over parts of Morocco I think, plus the fact that both countries are separated by like 10 kms of water only.
But there's a difference between Arabic influence on the Spanish language (which is quite obvious), and "genetical" influence or whatever; which is what the Coli obsesses about. Not all of nowadays Spain was under Arab rule, there's no reason to believe that every single conquistador had Arab blood. Actually quite the contrary since the Reconquista led to mass killings and exodus, wouldn't be surprised if lots of "mixed" people fled Spain, just like the Jews did. And the Conquistadores were not all from Spain (we all know Columbus was from nowadays north Italy).
And obviously when in Spain you will see what you call "Arabic" looking people...that's really Mediterannean looking people. That ocean has seen people going from one part to the other for thousands of years, it's no surprise they look similar.
Something totally different though is the Lebanese and other Middle-Easterners who emigrated to SA later on. But that has nothing to do with the whole Spaniard thing.