Doesn't this mean that modern medicine is pretty horrible though, apart from infant care? With all our know-how, theories, experience, tools, drugs, scanners, etc - we still basically aren't much better than ancient Greece?

Alternatively, it could mean our way of life is terrible and our medical knowledge is the only thing keeping us ahead.

Maybe, but if I didn't know we have similar life spans I would've guessed that modern life is far safer and healthier than ancient life. Some examples - better nutrition as evidenced by height and diet diversity, not drinking dirty water or eating dirty food, temperature controls, modern policing, not regularly exposed to dangerous animals or conditions, etc.