Not exactly. Statement usually goes towards Murata. Even the text speech bubble from Murata implies that other people than Murata have seeable breathing techniques.
This is a actual water attack. Tanjiro actually pauses to watch it slice through the tree and his blade wasn't attacking the tree.
To block Akaza's attacks, he had to use flame breathing which again is actually there. His sword was already by his side once he swung for the flame breathing to come.