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A close analysis of video of the debate supports that. At 1:26:35 in the video, Romney picks up the same white object—clearly a handkerchief this time—to wipe his face.
The Commission on Presidential Debates, which runs the debate logistics, did not release its contract of rules to the public this year. And it has not responded to request for comment on the 2012 debate rules. But a copy of the 2004 contract of rules reads: "No props, notes, charts, diagrams, or other writings or other tangible things may be brought into the debate by any candidate." The candidate can take notes, but only on a pad provided by commission staff.
As far as the rule on "tangible things," hankies appear to be an exception.