No competitive swimmer has the fear of drowning.
Here is why:
1. Most competitive swimmers can tread for at least an hours above the water without using their hands.
(Not BS, During the swim unit for my class I had to teach treading and I treaded for the full one hour and wasn't tired at the end of it. )
2. We do multiple exercises using a foam thing that goes between your legs called a Pull Buoy. This prevents us from using our legs and we paddle through the water at fairly fast rates.
3. We also use foam boards called kickboards and we hold them out infront and we keep kicking.
I'm pretty sure anyone who has been in competitive swimming for at least 6 months can stay above water for a while without using 2 of their limbs, maybe even three.
However for rowing, it's a different story