FEMA is part of DHS, yes. But it has its own bureaucracy and operates largely independently of the higher DHS bureaucracy. If FEMA is doing these things, it would not be inaccurate to say that DHS is doing them, but it would not be specific.

Think about it this way: If the FBI does something, do you expect the media to report that the Department of Justice did it? If the IRS does something, do you expect the media to report that the Treasury Department did it?