The first few chapters of Bala's book are mostly occupied with critiquing previous studies of the rise of science. Bala notes that when historians take up the "Why not there?" question in regard to some other society, they often wind up citing factors that could also apply to the West in the late Renaissance and early modern eras (when science emerged). For instance, the Chinese bureaucracy is sometimes critiqued for making society too orderly, but the Western European countries that made important contributions to the Scientific Revolution also had reasonably efficient civil services (except Italy, which gave us Galileo despite not having enjoyed orderly, punctual, and efficient bureaucracy since the Roman era).
Also, when critics get to the Greeks, instead of asking "Why didn't the ancient Greeks develop modern science?" the response is never "Well, they were deficient in X, Y, and Z..." but rather "Oh, come on, cut them some slack!" If the justification for the slack is the magnitude of their contributions, well, I certainly agree that the Greeks did amazing things for math and philosophy (and also technology, at least via Archimedes), but the Chinese had some pretty amazing technological achievements by the standards of the pre-scientific era. And the Muslims did a lot to preserve and extend Greek achievements, with Ibn Al Haytham decisively debunking some bad Greek ideas about light and vision. Why do historians respond to "Why not China?" or "Why not the Muslims?" with a list of defects rather than a list of excuses?
On the other hand, some historians apparently cut Greece some slack because of a perceived continuity between the Greeks and modern science. If the continuity is simply that the early modern scientists were influenced by the Greeks, well, yes, especially in regards to mathematics, but remember that Galileo's greatest achievement was to debunk Aristotelian physics rather than improve it. On the other hand, if it is perceived cultural continuity, I don't really know what that means. Modern science mostly came from Western Europe, not Greece. The Europeans who gave us science had a range of religious views, but they were mostly from Christian backgrounds (plus a handful of Jews), not pagan Greek backgrounds. If we're going to say that Aristotle and Newton came from the same culture then I think we have to include Mesopotamia and Egypt in that culture as well. The cultural lines from Mesopotamia and Egypt to Greece are at least as clear as those from Greece to England. Frankly, the English are weird. Separated from the Continent in multiple senses, they charted their own path after the collapse of Rome. They have a legal tradition built on Anglo-Saxon law rather than Roman law. They split from the Roman Catholic Church (and in a very different manner than the Greek Orthodox Christians). Even the language is weird compared to most other European tongues.
Besides the fact that Egypt and Mesopotamia gave us writing, arithmetic, geometry, agriculture, sailing, walled cities, etc. etc. etc., European culture was strongly influenced by an Abrahamic faith. Of course, Judaism had many differences from other Semitic religions, and Christianity picked up influences from Mithraism and Zoroastrianism, but if you want to go there you aren't going to find an argument that clearly separates Christianity from the Middle East, because Mithraism and Zoroastrianism have deep Iranian roots.
Anyway, that was a long digression on things besides the emergence of science, but if we're going to draw a line from Aristotle to Newton then we have to include a whole lot of other people in the same civilization. Otherwise we have to recognize that modern England and ancient Greece were two very different civilizations, and we can't cut the Greeks any slack that we wouldn't cut for other civilizations.
Besides, if the Greeks taught us anything, it's that you can be awesome at math and bad at physics. That's an important lesson.
One other thing that I learned from Bala: While Greek mystical and philosophical traditions treated the heavens as being very different from the earth, the Chinese treated them as being subject to the same principles. They would have been OK with Galileo finding mountains on the moon and moons around Jupiter, and Newton assuming that objects fall to earth for the same reason that the earth is attracted to the sun.