So what? This doesn't contradict what I'm saying, it confirms what I'm saying. He would end up with a 100 different songs because each piece of music (presuming they were all quite distinct) would suggest a different vocal melody. But it would still be the addition of the lyrics/vocal melody that transformed each of those 100 pieces of music into a song. That's the point. The music is not the song. Music is just music.
I can't comment on each of these names, as I'm not familiar with how they all worked, but in the case of Elton John as far as I know, he takes Bernie Taupin's lyrics and himself coins a vocal melody for them. So yes, Elton John would have created the song (song'writing' being a generally inaccurate description of how songs come into being anyway). But let's say, for the sake of argument, that all of these guys employed the same method as Morrissey/Marr (pretty sure that's not the case though - didn't Keith Richards write 'Angie' on his own for example?). But anyway, if such was the case, then of course yes, I'd say they weren't songwriters, they were music composers. Because yes, of course the same logic would apply. Why wouldn't it?
Again a misconception as you're assuming these two notions are mutually exclusive. They're not. Yes, I believe songs have music - or at least, they CAN have music, and music is usually what inspires a song's creation. But ironically in citing 'acapella' you're again underlining the point I'm making - songs don't NEED to have music. Once you have the vocal melody and lyric the song exists and doesn't depend on the music. It exist independently of the music. In other words, anyone can sing a song, unaccompanied by the music. If someone asks me to sing 'How Soon is Now' I don't need to say 'can't sing it, I don't have the music'. On the other hand, take away the vocal melody and lyric, and 'How Soon is Now' is no longer the song - it's just an instrumental, same as 'Oscillate Wildly' or 'The Draize Train'.
You in turn can argue all you like that Morrissey and Marr were joint equal creators of the SONGS of The Smiths. The onus is then on you to explain why Marr has not 'written' a great song since The Smiths broke up, whilst Morrissey has done so by the bucketload.