my take on this is that it is somewhere between a myth & an exaggeration - more than exaggeration, but not quite ungrounded enough to be myth. the problem is less about when people point to spain as a somewhat more literate society than existed around them, and more about when they try to give them credit for it, as the latter is mostly unjustified.
the video at least points out the importance of the byzantine influence, which is the missing ingredient in many of the narratives, which may credit the jews somewhat, but go something along the lines of "advanced arabs conquer primitive savages and protect spain from dark age, thereby creating renaissance". that sort of thinking is largely myth, but it's caricatured for a reason - you only really hear it from religious clerics and arab nationalists, whose voices are amplified by the contemporary culture, which trains us to defer to them rather than challenge then.
as mentioned previously, spain was a developed part of the empire, so anybody that took it over by force was given a pretty good head start in terms of building something new. it's consequently rather disingenuous to try to compare spain to france or britain, which spent the roman occupation period trying to overthrow imperialist rule. rather, you want to compare spain to other parts of the ancient world - italy, greece, egypt, the levant. and, how does spain fare when compared against it's contemporaries in alexandaria, or baghdad, or constantinople? not terribly, but not spectacularly. in that context, spain becomes it's name in arabic - the ass end of the earth. somewhat of a backwater, really...
i mean, one of the stories he mentions here is that the byzantines had to send monks to teach them to read greek - which is exactly the same problem that happened in italy, and exactly the thing that needed to be reversed to bring on the renaissance.
inventions like paper (which came from china) and base-10 numerals (which are indian in origin) may have come to europe through spain, but they may just as well have come through constantinople or even across the steppes. that spain was at the end of the trade routes shouldn't assign them any special status. and, al-khwarizmi was a persian in baghdad who was mostly reinterpreting existing greek science, rather than coming up with anything of his own - although he is one of a small number of persian and kurdish mathematicians that can be credited with original ideas (most of them, in truth, can actually not be - they were translators, rather than innovators).
on that note, it's worth pointing out why all these greek texts ended up in arabic in the first place.
when the muslims took over, they inherited a greek world - and inherit, they did. the arabs got all of the big libraries of the ancient world almost instantly, and nearly by chance. everything was written in greek. they seemed to realize that they'd just get conquered by the culture in the end, if they didn't uproot it. on top of that, they found a lot of disagreements in the existing greek literature, in terms of how it related to their new religion. they wanted a book burning, but they wanted to keep the good stuff, too.
so, what they actually did - and they did do this, as crazy as it sounds - is go through these huge libraries book-by-book and either burn the parts they didn't like or translate the parts they liked to arabic. once the texts by the authors they liked - which included aristotle, quite predominantly - were translated, the original greek was then burned.
so, we give the muslims credit for saving the books? no, they burnt the damned books! and, what was left had to be translated back from arabic, because they burned all the greek.
so, it's within that context that you have greek monks being sent to spain to teach the people there greek, after the culture had done everything they could to destroy it. did you think they just forgot because they were barbarians? no - the arabs burnt all the greek books, except the ones in the empire; there was no longer any utility in learning greek, unless you lived in greece. oops.
the fact that he has to bring in persian mathematicians and inventions from china and india, rather than point to the original work of intellectuals in islamic spain itself, should amplify the point - spain may have been doing fairly well when compared to the undeveloped areas outside of the empire, but it was actually largely a laggard within the remnants of the empire itself.
he hasn't brought up the renaissance myth yet...so i'll beat him to it...
while spain may have held some books, the event that really set off the renaissance was actually back-migration from constantinople to italy, which set in after 1204. the city was toast well before 1452, and people started leaving it, as refugees, in streams. some went north to russia, others in fact went to spain and the bulk of them went back to rome - because they were romans, in identity. they brought the more advanced culture of the late empire back to italy with them, and it mostly went from there. to the extent that anything found itself back to italy via spain in the arabic language, it would have been supplementary - and i don't want to downplay it, because that means it was probably the last chance to save it. but, it was the last chance, and not the driving influence. and, who created the problem in the first place?
what the arabs did leave spain was the culture of barbarism that developed in the region during and after the reconquista. the exaggerated almost-myth of islamic tolerance is really a reaction to the inquisition; it's a compare and contrast essay, but it misses the point - it was the arabs that laid the basis for the inquisition in their caste system of religious hierarchy, their extortion schemes and their punitive taxation. they seemed to have a thing for crucifying christians, they seemed to like the irony. worse, the extortion scheme is not "like organized crime"; this is the actual, historical origin of organized crime! it is the muslims that built the slave trade in africa that the spaniards would inherit and use to export africans to america - and they did it not based on the colour of their skin, but on the content of their religious observation. none of this would have happened if not for the arab presence, and their insistence on treating people differently based on their faith.
but, did some last gasp of empire, however perverted, hold out in the south of spain, no doubt in hopes of an eventual reunification with the fatherland? sure. for a while. just don't give it more credit than it earned - ground the analysis in actual fact, and realize that the similarities between spain and the rest of europe are pretty powerful as well, and that, while the peninsula may have experienced a less brutal dark age, it didn't escape it altogether. islamic spain was also a dark age society and should ultimately be treated like one.
so, this is better, but it's like he had a eureka moment when it clicked in that wait-a-minute, this is all bullshit. and, i wonder if he regrets publishing the first part of the series, if my analysis actually hits harder than i realized....