'This bottle doesn't have any water' was declared wrong and for me is the most natural translation. 'This bottle doesn't have the water', which is deemed acceptable, means that the water is in another bottle.
He is right about using "the" here. If one uses an article, it should be considered a mistake.
I thought "There is no water in this bottle" would be a better translation or at least one that sounds more natural, among the other possibilities previously mentioned on the comments bellow.
This sentence is so weird that we've finally decided to delete it and substitute with something else.