Yea, it was extremely unclear what the author meant by "age". If the author is defining the age of the water by the time the hydrogen bonded to the oxygen, and

Yea, it was extremely unclear what the author meant by "age". If the author is defining the age of the water by the time the hydrogen bonded to the oxygen, and the age of the sun by when it started fusing, then I presume you're right. Do you have a source for the claim that the majority of the Earth's liquid water has been through a photosynthesis cycle? Seems plausible but not obvious.