I would argue that if the C program didn't "create" the sound that it was certainly the musician responsible.
Fundamentally though, you are of course correct. This was a mainframe in the 80s, so presumably there was an operating system and system libraries and they all played a part, so should we credit those developers as well? it's tortoises all the way down.
Composers have a 'musical imagination' and often write at the keyboard of (typically) a piano. Classical composers sometimes write music that is not 'idiomatic' for a particular instrument; adjustments follow. From the original article it seems as if the composer had a definite idea of what he was after and adjusted things until he got close.
What interests me about the original anecdote is the use of random numbers in the parameters, and the difficulty that the composer had in reproducing a particular 'state' of the sample.
the THX sound was created by a synthesis program that was probably quite substantial itself (I have long been under the impression that it was a MUSIC-N derivative, and Moorer's description seems to confirm it) and, I'm guessing, probably not written in C. The input to this program was itself generated by a 20KLoc C program.
EDIT: i figured "i don't have to explain music-n, people can just look it up" but i just read the wikipedia article and i think that explanation only makes sense if you already know what it is. so...
MUSIC is a software synthesizer by Max Mathews, considered the father of computer music synthesis. It consists of a library of 'unit generators' and an orchestra/score processing system for using them. The "orchestra" file is used to define "instruments", basically parameterized combinations of unit generators, which themselves are basic synthesis building blocks (say, a square wave generator, or in the case of the THX sound, a wavetable oscillator).
The orchestra is controlled by a score, also known as a note list. This is just a series of statements saying, basically, "start playing instrument N at time T with parameters X,Y,Z".
MUSIC was followed by MUSIC-II, MUSIC-III, etc, hence the name "MUSIC-N". Basically every extant software synthesis package is derived from MUSIC-N on some level, but Csound is the most direct descendant.