People do say it, but I don't think anyone has drawn your attention to the distinction between genetic material and models of genetic information  before.  There is a reason that people refer to "the human genome" (notice, not any genome of an individual of the human species) using metaphors like "autobiography" or "compendium" or even more obviously, "code".  These are representations of objects (descriptions of a person's life, not the person), not the objects themselves. 

 The distinction is more common when people aren't comparing human to non-human animals, but are already focused on humansbecause of rights issues.  So, you might have to look in discussions where the applications of your perspective is known to have bad consequences (e.g., in the human genome diversity project).  Here is one example by a geneticist, that literally spells it out for you: 

 http://www.the-scientist.com/?articles.view/articleNo/32446/title/OpinionWhat-Is-the-Human-Genome/#articleComments