That's not the whole truth. Invaders came from far away Arabia, but they were few. From the top of my head, a few thousands.
Roman era Hispania was said to reach a million population. Not sure if that number declined during the Goths' kingdom (that were also a minority themselves) so the Arabians had to recruit 100k warriors of Maghribi origin to help them subjugate the peninsula.
When I hear "Moorish" (I'm Spanish, not an English native speaker, so not sure how they've come with that word) I suspect they're translating "un invento del tiempo de los moros" that would be more precisely translated as "an invention from the time of muslim Spain".
If it was invented here, it was a Spanish invention, no matter what the religion or ethnic group of the author was. If it was brought from outside, it would be interesting to know if it came from Arabia or the Maghreb.
I disagree that "moro" is a bad word in Spanish. It's just descriptive of NW Africa. Those countries are Morocco and Mauritania in English and I don't see their inhabitants protesting the names.
There's a weird projection phenomenom around denomyns: some people attribute ill intentions to perfectly natural names that the addressed people find fine. In Spain, I've heard someone upset about calling "Chinese" to... Chinese people and suggested calling them "Asian" or something like that because "Chinese" is derogatory. WTF?