Lord of The Rings: Fellowship of The Ring - Musical Boat Chairs
Toward the end of the movie, after the Fellowship has just left Lothlorien, there is a shot of Aragorn, Sam, and Frodo in one of the boats. Sam is clearly BEHIND Frodo. However, just seconds later, as Aragorn points out the huge statues,he grabs Frodo's shoulder, and you'll see that Frodo and Sam have now switched places in the boat.
The statues are not "around" the bend from Lothlorian. The journey took some time. It is reasonable to assume that they stopped and rested during the trip. at that time they could have easily switched positions.
The statues(i think they're called the Aragornath) are a few days travel from Lothlorien. Do you really want to see rowing down the Anduin and stopping, rowing and stopping some more!!Oh what fun!(NOT!)
If you look at Aragorn's shirt when they reach Amon Hen, he has his sleeves rolled up, so they obviously stopped earlier on. The trip didn't take the few minutes that they show in the movie - if it did they could have walked it!!
If you watch the movies that include the extended scenes, then you see that the party stops for a night and Frodo and Sam take the "switched" places the next day.