When is Water Produced During Photosynthesis?
Some of the water that's split is regenerated when the hydroxyl radicals (reactive oxygen species) are converted to hydrogen peroxide, water, etc. by superoxide dismutases and antioxidative mechanisms in the chloroplast (peroxisomes/catalases, etc. take care of this). There's also some evidence that the presence of mannitol, ascorbate and glutathione protect against ROS produced in chloroplasts as well. So you input water, and in an effort to avoid oxidative damage, you do get some water generated. However, the balanced equation doesn't reflect this because it's not an actual product of photosynthesis.

About ROS and protective elements

Extra Reading on ROS in photosynthetic systems

I think that's a very obscure fact, and despite the reality of things, it's actually difficult to query the literature. Good question.