I would not consider a D4P a checkerboard. To me a checkerboard is just that, alternating squares of red and white. I do like the idea of the gradating color. I would have her look at pinterest red and white quilts and see if something stands out to her. The Vortex quilt pictured here:
http://folkartmuseum.org/exhibitions...-white-quilts/ is one of my favorites and on my someday list but I wouldn't consider this a checkerboard either, however I think it is a closer approximation of a checkerboard than a D4P. Even DIC or TIC would be more checkerboard-esque than a D4P. But that said, people who don't quilt and don't know how to describe something sometimes come up with some pretty offbeat ways to say what they think they mean. She could mean she wants a red and white quilt in squares and rectangles only, as opposed to say star type quilts.
another thing you can consider, Piece it like a checkerboard with smaller squars but quilt is as though it were a whole cloth, ignoring the piecing entirely. I have seen many a stunning quilt done that way.