[0] http://www.theguardian.com/technology/2014/mar/28/which-phon...
I was talking about passive signal noise which could be used to locate a potential target (e.g. pick the president's vehicle from the identical ones in the motorcade). Even a hardened phone will still leak EM radiation.
If we're talking about informational security, well, I don't know why we would. The Fitbit doesn't sync realtime and most of the president's meetings are public. So while it would be extremely embarrassing, I don't know how compromising it would be.
Though I thought not having a phone for anti-tracking is strange as he borrowed his aides phone for the photos. So couldn't 'whoever' simply track his inner circles phones? In which case he may as well carry a phone and an agent secures the phone for anything where tracking could be an issue?