The vast majority of people are religious. Science is a religion. Religions can be better or worse. Religions differ by focus. The ultimate way to judge a religion is by outcomes. Science is a good religion. So is Christianity, in a different way. So is Judaism, in an entirely different way. So was Islam in a way very similar to Christianity (something became broken in Islam after the defeat in Spain and I am not sure what). So was the Egyptian cult of Amon-Ra, etc. On the other hand, the Semitic cults of Ba`al and Ishtar as well as the Greek and Roman religions were not so good. Pagan cults of place spirits and such were quite lousy.
While religions can be good or bad, religious fanatics are almost always harmful. The traits of religious fanatics are (i) fixation on their religion and (ii) claims that all other religions are false. Richard Dawkins, for example, is a religious fanatic of atheism. (Atheism is distinct from science [science has nothing to say on supernatural beings, but atheism does], also a religion, and a rather useless one, about the level of the cult of Ishtar.)
To answer your original question: the tendentious history of science that you refer to is what the New Testament is to the history of Christianity. It’s not that it’s wrong, but it’s not where you’d look for an unbiased examination.
Practice science by all means, but not religious fanaticism of science. I’m afraid it may be the latter that informs the sentiment of this post.
What may have been different about the Greeks is an unusual extent of religious tolerance they had. Their basic view was diametrically opposed to religious fundamentalism—instead of treating other religions as false by default, they treated them as true. To reconcile, they mapped every religion to their own with much flexibility. (Most affected religions were enlightened by this attitude of tolerance. But, for example, the exclusionary Judaism, inherently fundamentalist [look at the first commandment again] was less ready to embrace the Greek mapping.)
(Because I also don’t believe in unbiased analysis, for the context: Personally, I consider myself an agnostic. This includes my attitude towards science. Or perhaps I’m a math cultist. I’m also culturally Jewish.)