I have found myself able to breathe while being completely under water. This has occurred in various situations, however, I performed a controlled experiment in a superflat world and easily recreated the bug. I built a 1x1 vertical shaft 3 blocks high and placed a water source block in the very top of the shaft. The water flows down the shaft like normal. However, when I switched to survival mode and dropped into the shaft, I consumed air like normal and my vision changed while my head was in the source block, but as soon as I dropped through it, landing at the bottom of the shaft, I could breathe and my vision looked like I was above water. I could still swim and was still pushed by the current, but I could breathe. 

This caused:
1. Can't drown.
2. No swimming animation.
3. No underwater screen status(water texture).
4. Items do not float.