"Ms. Bovbjerg, though, said those figures don't take into account the estimated 5 million illegal immigrants from Mexico currently living in the United States or the millions who have lived in the United States but have since returned to Mexico."
I think the main points of the discussion are all internally consistent: 1) Bobvjerg criticizes the SSA estimate. 2) Barnhart states that under current law anyone receiving SS benefits must be a legal resident of the country being lived in at the time the benefits are paid. 3)The reporter summarizes lawmakers and witnesses as pointing out that under the law illegals working in the U.S. and then returning to Mexico are not excluded since they would be legally living in Mexico at the time benefits are received. (Note they are not claiming illegals living in the United States would receive benefits.)
If there is a source somewhere that documents that this agreement is definitely limited only to legal Mexican immigrants, I would consider it. FWIW, I don't buy the notion that there is a secret plan for this to be a big campaign surprise, but I think there is probably a problem here.