Okay, this question has been unanswered long enough. I call movie mistake!
I'll use two different articles to defend my claim. Firstly, this article describes the primary filming location - The Pelorus River.
However, a second article I've found involves an interview with Peter Jackson about the creation of this scene. This was Peter Jackson had to say:
How tough was it to shoot the centerpiece action sequence with the
Jackson: We had these big V8 water-jet things that we
built on a circle – it was like a theme park – about as big as this
room. And we were worried because we thought, how fast can we actually
grind, wind the engine up, because we could sort of wind it up at
speed and, you know, we’d better be careful, you know, because we
don’t know quite, it’s gonna be unpredictable and it was. And we had
stunt guys doing it, round and round, and testing it and everything
else, but you know, these are actors, they’re a little bit fragile
(laughter). But by the end of the first day, the guys were just
yelling, “Faster! Faster! Get it faster, faster, faster!” And we had
it on max, we had the thing going on maximum pretty quickly.
But one of the things that doesn’t really get referenced in the
barrels is we also did another shoot on a different river in New
Zealand, called the Awatere River in the North Island. And that was a
shoot where – that’s a particular river, it’s like a gorge or a
canyon, a rocky canyon that stretches about a mile and right at the
head of the canyon is a big dam, and four times a day they open up the
sluice gates and they just let this enormous torrent of water out, and
they let it out for 10 minutes and then they close the gates again.
And so we got a lot of the really kind of hair-raising barrel stuff in
the Awatere. It would be too dangerous to put a stunt guy down. I
mean, we didn’t even dare put anyone in the barrels. We sent the
barrels down completely empty and we put the digital Dwarves in later.
But that got some of the more dramatic footage, was this – and it was
just, it was great because we could set up the cameras when it was dry
in between the dumps and we set up about six cameras right the way
down the length of the gorge, and then we were there for about three
days and every single, you know, four times a day on the dot, these
things would open for 10 minutes. And we had a team up, throwing the
barrels in, at the top. And we had another guys – you didn’t know what
the hell was gonna happen to them, you had just to – they just were
filmed on the way down and we had a team at the bottom recovering the
barrels. We lost three of them. I mean, to this day, we don’t know
where three of those barrels have gone.
I've italicised a few sections for effect. Effectively, the shoot was done in multiple locations, on multiple days, involving fast moving water, with the actors later super-imposed in for the most dangerous parts.
Given all this, it seems highly possible that it was a simply movie mistake. Whilst now it has been alluded to in this thread (and to me at least, it sticks out like a sore thumb everytime I rewatch the scene), this has been highlighted almost nowhere else online (e.g. Movie Mistakes). Unless you're really paying attention, it's easy to gloss over which is my assumption as to why it wasn't spotted.
I can provide no definitive evidence, just opinion - it seems very much like a simple movie mistake.