Regardless, I'm not sure that I agree with you that a musician should write her songs in order to be called an artist.
To be called a musician one should at least be able to do one of the following:
- Songwriting
- Composing
- Playing one or more instruments
- Singing
Many "musicians" that were mentioned in this thread already aren't able to do any of these, since they rely solely on a skilled marketing team and a producer that is able to convert a dog fart into harp music.