Well, it's not to do with the likelihood of a particular thing having/having not existed--your point there is well-taken on that front and I agree. Its to do with the practicality of the characters using that thing under certain circumstances.

Evidently (according to my amateur findings anyway, though I'm glad to defer to nautical experts if such are in the ranks) lateen-rigged sails were used in situations where the wind would shift or where they might have to go against the wind; whereas square-rigged sails were most efficient for open sea situations with the wind behind the ship, which is exactly what's up with the ship under consideration here.