it's just a question of credits
I understand your point and it is a valid one. I just meant that from a strictly listening standpoint it's mostly moot, although for historical purposes it is something to be curious about. If anyone would really be concerned about composing credit it would be Kenny Clarke, since Sonny seems to have gotten the major fame for that tune, although I doubt very much in the way of royalties.
Here's the Rue Chaptal recording that SIB1707 mentioned above, and as one can see in the video, the label credits Clarke. That was recorded in 1946 which predates Sonny's version by 10 years. However, since Klook has been dead for 26 years and probably doesn't care, it's kind of late in the game for changing the attribution, unless his descendents cared about it.
I'm looking at the original record of
Tenor Madness right now (had it since about 1961) and yes the song has that same title and is credited to Sonny right there in black on the yellow Prestige label. (It also says "John Coltrane, Tenor -- Guest")
Clearly someone at Prestige gave the composing credit to Sonny, so what are the possible reasons? Either, a) Sonny actually said he wrote the tune and took credit for it, b) Bob Weinstock, Rudy Van Gelder, or someone else at Prestige mistakenly gave him credit, or c) something else. However, how does one find out?
Other than Sonny himself, Bob Weinstock and everyone who played on the Tenor Madness sessions is dead and not talking. So, I suppose one could write Sonny and ask him directly about that, and who knows, he might be willing to explain it. Barring that, Rudy Van Gelder is the only other person still alive who was involved with the Prestige sessions and might know something about the subject. For a jazz historian it might be worth it to try and ask Sonny and/or him about it.
Me, I just like the tune and enjoy listening to all these versions of it.