Although, after doing some more searching for the actual law, it turns up this:
§930. Possession of firearms and dangerous weapons in Federal facilities
(a) Except as provided in subsection (d), whoever knowingly possesses or causes to be present a firearm or other dangerous weapon in a Federal facility (other than a Federal court facility), or attempts to do so, shall be fined under this title or imprisoned not more than 1 year, or both.
(b) Whoever, with intent that a firearm or other dangerous weapon be used in the commission of a crime, knowingly possesses or causes to be present such firearm or dangerous weapon in a Federal facility, or attempts to do so, shall be fined under this title or imprisoned not more than 5 years, or both.
© A person who kills any person in the course of a violation of subsection (a) or (b), or in the course of an attack on a Federal facility involving the use of a firearm or other dangerous weapon, or attempts or conspires to do such an act, shall be punished as provided in sections 1111, 1112, 1113, and 1117.
(d) Subsection (a) shall not apply to—
(1) the lawful performance of official duties by an officer, agent, or employee of the United States, a State, or a political subdivision thereof, who is authorized by law to engage in or supervise the prevention, detection, investigation, or prosecution of any violation of law;
(2) the possession of a firearm or other dangerous weapon by a Federal official or a member of the Armed Forces if such possession is authorized by law; or
(3) the lawful carrying of firearms or other dangerous weapons in a Federal facility incident to hunting or other lawful purposes.
Kind of long, but even if he was not there on “official business,” section d(3) would seem to be a catch-all for otherwise lawful carry as long as the purpose is, well, lawful.