I pulled my copies. Here’s the deal:
1st edition paperback: copyright 1953, then “in association with Ballantine Books, Inc, Houghton Mifflin Company Boston, 1954,” presumably referring to the publication date. Then on a separate page: “A hardbound edition of this book, priced at $2.00, may be obtained at your local bookstore.”
1st edition hardcover: copyright 1953, then “1954 Houghton Mifflin Company Boston,” presumably referring to the publication date. Then also there’s a blurb that reads, “This new book published initially in two editions by Houghton Mifflin Company…” Below that, in a second paragraph, it says, “This simultaneous publication makes new books widely available at low prices, and we believe that it is an important development in American publishing.” (emphasis added)
So it looks like the book was finished and copyrighted in ‘53, but not published until the following year. And when that happened, the book came out in paper and hardcover at the same time.