To say that the Greeks didn't have correct scientific theories is obviously true. To say that they had a methodology that departs from ours is somewhat true. To say that they were merely making stuff up without reference to any observation is to merely make stuff up without reference to any observation. I could do someone significant bodily harm by hitting them with Aristotle's collected empirical works on the anatomies, reproductive systems, social habits, and forms of locomotion of animals. And I'm not a huge dude.

"Virtue" has a specific meaning in the ancient Greek world which doesn't seem like it's all that relevant here. The way I would put it is that a clever Greek interested in the natural world became an engineer, and a clever Greek interested in the social world became an active citizen, which is a sort of combination of landlord, lawyer, and philosopher. Archimedes made his living by basically being the iron-punk hero of Syracuse; Plato and Aristotle made their living by teaching young rich folks how to be effective rich adults. A broad-minded citizen should be curious about the natural world, but curiosity is just a hobby, not a calling.