It seems that you were right from the ASCAP's point of view, see The Birds & The Bees:
... 13. The Great Speckled Bird
Words and music: Traditional American
I hesitate to put The Great Speckled Bird in the Public Domain section because the most famous version, by Roy Carter (a pseudonym of Vaughn Horton) and performed by Roy Acuff, is a copyrighted arrangement and an ASCAP composition. At least one source says that the song was about 40 years old in 1950, and that it was popular with Holy Rollers. Other sources credit it to Guy Smith, a radio entertainer from Springfield, Missouri who was known as Uncle George. At last count, BMI lists 19 versions of the song, including one by Guy Smith; ASCAP lists 5. Roy Acuff copyrighted his own version in 1937, but it is set to a melody that no one would recognize. The Great Speckled Bird is most often sung to a tune that is pretty close to A.P. Carter's 1929 song I'm Thinking Tonight Of My Blue Eyes. Artists with copyrighted arrangements of The Great Speckled Bird include Johnny Cash, Rose Maddox, Charlie Monroe, Harvey Reid, William York, and others.
As there is no known original record label from the 1930s or 1940s of Roy Acuff's recording with the "Roy Carter" copyright (and there's nothing on Vaughn Horton's AMG page about it), I assume that it should not be in the notes here. (I 'd rather say that Roy Carter is a fictional character with the names of Roy Acuff and A. P. Carter mixed.)
I've listed the information pertaining to "The Great Speckled Bird" according to the accreditation provided for the title and performer within the ASCAP database. If they are in error, I would suggest taking it up with them.
Hi Twitster, another dubious composer credit here in your notes for A1. As far as I see, none of Acuff's commercial issues of this song in the 1930s and 1940s (and there were many) had any credits, and if they had, they would definitely not have credited "Roy Carter". There is an undisputed writer of the lyrics, Reverend Guy Smith, but the melody is apparently traditional. It was used before by the Carter Family for their song "I'm Thinking Tonight of My Blue Eyes" in 1929, but they were not even the first to use it for a recording. So even when A. P. Carter (not a Roy) grabbed the composer credits for the Carter Family's recording, he was anything but the composer of "The Great Speckled Bird".
See here for the Carter Family's record and later songs with the same melody: V-40089.