And when I say I have to I really mean that: I'm Dutch, tried studying physics, dropped out, switched to studying art, specifically photography (even built my own camera at one point), then in the first year of art school was introduced to the Hockney-Falco thesis, then went to the International Congress of Physics Students one last time to hang out with my friends, decided to give a talk on the topic, and ended up winning best talk of the conference. So I'm kind of obliged to Have Some Opinions on this topic.
The clip mentions the HF thesis as if Hockney introduced the notion that the Dutch painters in Vermeer's time used optical tools. That's... not what the thesis claimed. Johannes Vermeer lived in the 17th century[2]. As the clip (correctly) states, telescopes and mirrors were known to the Netherlands by then - in fact the earliest known records of a refracting telescope is from a failed patent application in the Netherlands in 1608[3].
From what I remember, the hypothesis that Vermeer used optical tools wasn't controversial even back in the mid-2000s, a decade before this film came out. While there was no direct proof, he did live in the right place and period to have been introduced to telescopes, and artists trying out new tools is obviously a thing that happened throughout history. Being secretive about his work was obviously also very suspicious. I recall that we also discussed how certain visual qualities of the painting suggested the use of optical tools - Vermeer's style was also just so noticeably different and photograph-like compared to his peers. To be clear, nobody thought this diminished the quality of Vermeer's paintings: he was still innovating and mastering his tools, and creating the beautiful paintings that he made still took tremendous skill.
However, what the Hockney-Falco thesis claims is that Early Renaissance painters like, say, Jan van Eyck[4] already used optical tools, centuries before telescopes and optical mirrors optics were introduced in Europe. We're talking 15th century onwards. And not only that, that this was secret knowledge hidden by the painter's guilds, of which no known record survives even though we have records of all the other painting techniques used. That's what makes it so controversial.
The hypothesis that there was a painter who lived during a time of great innovation in optical tools in the place where those innovations took place, then secretly used those tools to get a leg up on the competition is very plausible.
The suggestion that the entirety of Europe's Renaissance painters learned about optical tools from Arab lands but managed to keep this knowledge secret for centuries sounds like a conspiracy theory.
(also, it's completely ignorant of the realistic qualities of some of the old Roman art[5], and those painters definitely did not have high quality lenses available to them)
[0] https://www.youtube.com/watch?v=XoqWwuRnj3o
[1] https://en.wikipedia.org/wiki/Hockney%E2%80%93Falco_thesis
[2] https://en.wikipedia.org/wiki/Johannes_Vermeer
[3] https://en.wikipedia.org/wiki/History_of_the_telescope