It's saying far more than that: it's saying that the DNA changes according to the needs and functions of specific cells.
What that means is, there is something that controls that change: a mechanism that alters DNA according to specific function. So what is that mechanism? How does it work, and from where does the relevant information come?
That's a very interesting question, which may be answered by the discoveries that have been accumulating about "meta information" within the DNA: information may be encoded "above" the single-gene level. My simple-minded analogy would be that the individual genes represent syllables, and the meta-data represents words of one or several syllables....
It could be that DNA codes the most basic processes for a cell and that as the cells themselves reproduce in their given areas, complete with mutations, that the cells themselves adapt and evolve to fit in their niche in the body. In this case, there need be no meta-information stored anywhere--the process relies on natural selection to pick the best cells for the functions they are supposed to perform, and those that don't are reabsorbed by the body.
Following this logic to its end, when these processes go awry, you get autoimmune disorders or cancers. Maybe they are the flip sides of the same process, where an autoimmune disorder is the body eating itself because something didn't evolve properly and all the cells get targeted for removal. Then cancers would be the case where the cells mutated too well and outsmarted the body's ability to keep them in check.