This probably isn't going to be a very productive argument, since we're just debating the definition of a phrase, but whatever. I apologize if this seems condescending, but I just want to take a simple approach to avoid spinning off into a debate that's more complicated than it needs to be.
"Avant garde" literally means "advance guard," as in the guys in front; in practice it's a term that indicates anything which pushes the norm or is pioneering or "cutting edge," usually (but not always) in an artistic sense. It isn't a genre of music, or a term indicating a state of "genre-less-ness," it's just a descriptor for something that pushes the limits of the norm.
So, you can have a band that recognizably plays a given style, but innovates in enough ways that they could be referred to as "avant garde."
To be honest, "progressive" has a lot more genre-label connotations than "avant garde."