I consider myself to be a citizen of the state of Arizona, which entitles me to various privileges and legal considerations, but I am also a citizen of the United States. If some governmental entity in my state were to either attempt to deprive me, specifically, of a right that I felt I had as an American citizen, or to deprive all Arizonans of such a right, whether by statute, or by executive or judicial action, I should not have to leave my home and move to another jurisdiction in order to exercise that right.
In other words, it is sometimes necessary for the people to seek justice from outside their home state, and that's where intervention by federal authorities may be justified...just as might be necessary if my city or county sought to deprive me of some right I ought to be able to exercise as a citizen of the state of Arizona.