Your query sent me into a small pile of ancient "Schwann Long Playing Record Catalogs" I still have (why, I ask myself, do I keep all this stuff around?!), and this album is listed there under Basie's name, interestingly (not Bennett's) as "Basie Swings, Bennett Sings." Schwann generally shortened album titles to fit the catalog, but the fact that they didn't shorten it to "Bennett/Basie" supports your contention that the longer title may have been the intended one.
Edit to add that this particular catalog dates from April 1964.
gregmo