Her statement is correct - Fleetwood Mac is her band in that she is a member of FM
I think your assumption is that she means or implies that FM is her band in the sense that she owns it. I think this is incorrect. I base this on her statements to this effect last year around this time when she said "Mick and John could fire LB and me and start over - they are FM."
Also, most artist I have ever known, and I have known a few even some very famous ones, are very quick to let you know they are an artist
Plus, I think Stevie saying she is a songwriter or poet is just like someone saying I am a mechanic. Is she not supposed to say what she does