The camera was mounted on the lunar module; it was not being held by anyone. If my memory serves me correctly, current safety standards are much more stringent than they were for the first lunar mission.
From the link I posted:
Armstrong’s descent was captured, not by a “cameraman” but by a camera placed in the Modularized Equipment Stowage Assembly (MESA), a compartment near the ladder, and deployed by Armstrong as he was standing on the Lunar Module’s porch. The original camera that was used was left on the moon.
reply