Not at all. In fact, it hasn't got much to do with writing music.
Being a good musician involves visualizing the song or even the set or the band as a whole, and doing your part to make it sound the best. It involves an understanding of what instruments, vocalization and dynamics sound good at a particular part of the song, and for the song as a whole. Being a good musician means knowing how to find a tone for your specific instrument that doesn't clash with the other instruments, and knowing how to not play over the vocals. It means that you know how to apply dynamics on the fly, and how to recover when you or someone else messes up. It means you know when to back off, when to let other instruments or the vocals shine, and when you need to step it up and be out front. It even can involve understanding acoustics, the technical aspects of a PA system, and how other instruments work, sound and behave. It can have something to do with writing songs, but in general, it doesn't have much to do with it.
It's stuff that can happen naturally with people who have a good ear, a good vision for music, and can quickly figure out how to produce it in a practical manner. However, it usually comes after a whole lot of sweat, practice, and years (more like decades) of making music.