Then they are poorly named, "Center for Disease Control" pretty much says that they are there to help CONTROL diseases which is a pretty specific job description. Their name pretty much describes what their primary mission should be. That, to me anyway, means that they are there to come up with responses to things like this as well as help develop vaccines and other cures.
The Health Department (from the Surgeon General on down) are there to implement the recommendations of the CDC and others, by force if needed (that's why health department officials are officially considered the equivalent of officers in the military just so they can give legal orders).
If you meant that there has been mission creep from controlling disease into other areas at the expense of their primary mission I wouldn't disagree but to say that it's not in their normal job description I would have to disagree.