Has Sean Carroll refuted the fine-tuning argument?

The first of five in an interview series between Luke Barnes and Allen Hainline responding to atheist and physicist Sean Carroll (Ph.D., Harvard):

By the way, Luke Barnes is great. His book A Fortunate Universe, co-authored with his colleague Geraint Lewis, is likewise great. Robin Collins (Ph.D., University of Notre Dame), one of the world's foremost experts on the fine-tuning argument, has said about the book:

Lewis and Barnes' book is the most up-to-date, accurate, and comprehensive explication of the evidence that the universe is fine-tuned for life. It is also among the two most philosophically sophisticated treatments, all the while being accessible to a non-academic audience. I strongly recommend this book.

I follow Barnes' weblog Letters to Nature as well as his YouTube channel Alas, Lewis & Barnes. Barnes has done a number of interviews including with Robert Lawrence Kuhn at Closer to Truth.

If I recall, Lewis is an atheist or agnostic, while Barnes is an evangelical Anglican. Both are physicists (cosmologists) with doctorates from the University of Cambridge, U.K., and both are professors in Sydney, Australia.

Barnes and Lewis have a forthcoming book with Cambridge University Press: The Cosmic Revolutionary’s Handbook (Or: How to Beat the Big Bang).

Edit. Part 2 is available below.