Your problem is that you are confusing song-writing and performance/arrangement. The notion that because Steven played drums on demos before Matt recorded them for the album, therefore Steven wrote the song - that is just wrong. It is just like the Izzy/Gilby thing. No, Gilby gets no song-writing credit for his contributions. But he certainly changed some of the guitar performance/arrangements from what Izzy had done. Izzy's song-writing credit is completely separate from his guitar performance/arrangements. The same applies for Steven and Matt.
Maybe you're getting confused by the fact that for AFD and Lies, the band gave song-writing credits to all five members, whereas on UYI they did it by writer only. For example, Slash/Duff/Steven had nothing to do with writing Anything Goes, but they got song-writing credit for it anyway. Doesn't mean they actually wrote it. That was just a business decision (kind of like how every Beatles song written by Lennon or McCartney is credited Lennon/McCartney, regardless of whether both guys wrote the song or just one). I think that the members of GN'R generally prepared their own performance/arrangement during recording sessions (other than the instances where we know they didn't, like Matt's drumming on November Rain).
As for how song-writing credit normally works, go read what I wrote again. It matches your explanation (although you shouldn't forget, musicians get song-writing credits separate from their performance/arrangement, like how Duff wrote So Fine or how Matt wrote the main guitar riff to Velvet Revolver's Set Me Free).
You dont know what you are talking about. Adler was fired from gnr because he couldnt perform the songs in the studio. It took him 30 or 40 takes just to do civil war when they were working on that nobodies child album that Axl had to piece together.
AFter that they went into the studio to record UYI and Adler was always high. The songs were already written at that point. They just had to record them. Adler was then fired and Sorum was brought in to record the album. He didnt write with the band. Anything he may have written he just improved upon what Adler already wrote. Why cant you understand that?
As for AFD, on the booklet they credit everyone but they also had it written down for who the true song writers were for royalties. And it went like this
Welcome to the Jungle -
Music : Slash, Rose
Lyrics : Rose
It's So Easy -
Music : McKagan, Arkeen
Lyrics : McKagan, Arkeen
Nightrain -
Music : Stradlin', McKagan, Rose, Slash
Lyrics : McKagan, Rose
Out Ta Get Me -
Music : Slash, Rose, Stradlin'
Lyrics : Rose, Stradlin'
Mr. Brownstone -
Music : Stradlin', Slash
Lyrics : Stradlin'
Paradise City -
Music : McKagan, Slash, Rose, Stradlin'
Lyrics : Rose, McKagan
My Michelle -
Music : Rose, Stradlin'
Lyrics : Rose
Think About You -
Music : Stradlin'
Lyrics : Stradlin'
Sweet Child O' Mine -
Music : Rose, Slash, Stradlin'
Lyrics : Rose
You're Crazy -
Music : Slash, Stradlin', Rose
Lyrics : Rose, Stradlin'
Anything Goes -
Music : Stradlin', Rose, Webber
Lyrics : Stradlin', Rose
Rocket Queen -
Music : Rose, Slash, Stradlin'
Lyrics : Rose