All of the information that you cite is correct. Although it should be noted that the original 45 release does list both “C. Adams” and “B.B. King” as composers.
However, that being said, I would like to clarify the information cited from the book –
The names that appear after the songs titles of numbers that Green and Fleetwood Mac covered are the names of the performers whose version of the song they mostly drew from.
In example, the name after ‘Homework’ is Otis Rush, not, Al Perkins, who wrote the song.
I realize that this may seem unfair to the composers, but in the case of many of the songs, the versions that inspired them was itself a cover of an earlier version.
It is interesting that you zeroed in on ‘All Over Again’ as almost all references found now on the Internet list the song as “Traditional”.
This seems to be because that was how it was listed, and continues to be listed on the second Paul Butterfield Blues Band LP, “East – West” which came out less than a year after the King recording. Compilations containing the Butterfield recording continue to list it this way.
I have put up “Part One” of a post concerning the history of the song on the book site – https://smilingcorgipress.com/catego...er-the-covers/
- with some duplication of the details provided by Krzysztof.
I thank you for your kind words and I will also be putting up a section (a hopefully small section) on the site where I can post corrections to any errors that sharp-eyed (and sharp-eared) readers may find.