You are probably right in saying everyone is influenced by other's music. My just playing the guitar was influenced by others, but I don't hear something and try to duplicate it and claim as mine. I might learn a song or even change it, but it's not mine. I have rewritten lyrics to existing music, but I don't claim it as mine. Same goes when I rewrite the music.
I'm working on a song now that I heard a guy do live at the Peace Cafe in Dayton, Ohio. I liked the lyrics (somewhat), but did not like the way he played or sang it. So, I am rewriting all the music and changing some lyrics, but I will not claim it as mine. He was the originator.
So, I guess you can say I was influenced my is song.