I really enjoyed this book, but I also felt slightly disappointed. I'm not very familiar with the Renaissance or many of the movements discussed -- humanism, atomism, Epicureanism, and it was fascinating. But I felt that Greenblatt's concentration on the impact of De Rerum Naturum on a few selected people left me with little understanding of the period generally. I think he did a little better history with the Greek and Roman periods which resulted in the poem. Now I'm going to have to find a more comprehensive history of the Renaissance to read.
As for whether the author proved the impact of Lucretius on making the world "modern", I agree the subtitle may be hyperbole, but I think Greenblatt's view is that it was a more subtle but indelible influence. Remember that a "swerve" is a minimal change in direction. Lucretius was being read by most of the scholars and intellectuals of the next few centuries and it encouraged them to question established thinking.