It was not entirely uncommon for one to speak in third person. In this instance, it is entirely possible that Smith did so because he had an uncommonly large ego and wished to make himself look more important that way. He was known to exaggerate his own importance and gallantry on several occasions. The following quote, taken from wikipedia, indicates the self-importance he ascribed to himself. He is speaking of the Powhatan Indians.
He was friendly toward them, but never let them forget the might of English weapons… Realizing that the very existence of the colony depended on peace, he never thought of trying to exterminate the natives. Only after his departure were there bitter wars and massacres, the natural results of a more hostile policy.
Incidentally, the entire Pocahontas fable was of Smith's creation. There is some evidence that she intervened before an axe fell on his neck, but this was a preplanned performance by the Indians. Pocahontas at the time was about nine years old. Only when she went to England with her husband, John Rolfe, and where she was quite popular, did Smith invent the story of the failed romance.