As I watched this documentary I couldn't help wondering: Was the Qur'an a help or a hinderance to these unquestionably great minds of the Middle Ages?
Perhaps a bit of both. The Qur'an was a catalyst that drove the Arabs to build a huge empire and motivated many great minds to study and learning. As they say; 'Science follows the money' and science thrived under enlightened Caliphs and Amirs.
Its very interesting. I think you are right - conditions on the ground, resources and stability in a certain era, and an openness to translation and knowledge transfer all contributed to this. But I find wondering about whether the Quran was a possible catalyst for this, to be problematic. For example, is Chinese scientific achievement in ancient times ascribed to innate qualities of Confucian texts or the Dhamapadda? Or Indian scientific and mathematical discoveries, ascribable to the bhagavad gita? At some level, its just reductive to frame it in these terms, and even asks the question on the ground of those who want to elevate the Quran to a level where it can be made responsible for all that is good in humankind.
Science flourishes where there is:
(1) Cosmopolitanism
(2) Stability
(3) Intellectual resources
(4) Material resources and patronage devoted to scientific study
(5) The support and tolerance towards free thinking and scepticism
(6) Openness to opposing views and cultures
I think these are the basic conditions that have prevailed to a greater or lesser extent in places and times in history in many different realms - from Asia, China, India, Arabia, Persia, Greece, Europe, America - sometimes in small pockets, sometimes on a wide scale.
I think that if those conditions and values are not priveliged or valued, then there is a closing of the mind, and consequently, of science. I think the 'Golden Age' of Islamic domains had a period when in certain city states and areas some of these conditions prevailed. But then the mind closed, the literalists prevailed, and these conditions and ideas even today struggle to prevail in large parts (possibly the mainstream) of the modern ummah civilisation too.