Yes, the statement is incorrect. Nevertheless, it has two possible ways of being corrected. On the one hand, it is possible to be corrected as: "St. Leger traveled up the St. Lawrence River on the way from Montreal to Ft. Oswgo. It is so because of direction of the river current.
As well as that, it is possible to correct the statement as: "St. Leger travel up the St. Lawrence River on the way from Ottawa to Ft. Oswego". In this case, it is so because the travel that St. Leger did on the St. Lawrence River, was part of the Saratoga campaign which was organized by British army for going from Ottawa to the south for reaching the Hudson River surroundings to gain control in the region.