I think writing with, and writing seperate from each other are way different things. One guy writes a lyric on a paper, and hands it to a musician. That's more like pin the tail on the donkey.

Writing with the music rolling is much different, thats probably how most do it, but most lyrics people are not very good at that.

The doors are one of the few rock bands that set music to lyrics, and thats cause Morrison wrote poetry, and the music was backdrop for the poetry.

I guess its all co writing, but with bands, it's more collaborating and arranging.

Either way, if somebody is traveling to Nashville in hopes of writing with a pro writer, that has little to do with writing, that has more to do with networking and marketing to make a career out of it