The article said this was done by Janet Napolitano's staff. Napolitano is the former Democratic governor of Arizona who was put in place by Obama, so I think it's fair to criticize him here.
Bush did have issues with FOIA, though, but they were quite different from investigating the politics of people making requests. Specifically, under Bush, agencies were supposed to deny as many requests as possible. I don't believe Bush ever had the DHS looking into who was requesting what (at least, not that we know of). After all, the DHS had no permanent leadership until Obama appointed Napolitano.