I have been talking about this article with some of my colleagues lately.
It is possible for it to move especially in areas that are prone to soil erosion (delta areas typically have a lot of top soil and can tend to have higher run off from soil texture and lack of structure, along with increased irrigation, rainfall, and drainage). In the field in contact with soil glyphosate has a half life of 2 days in optimal conditions. If conditions are less than optimal the half life could be as high as 174 days which isn't really that bad. In aquatic conditions glyphosate has a half life of less than 7 days.
see page 7 hereThe article talks about the degradation product of glyphosate. Without doing much research on this (I will check in to it sometime this week) I don't know much about it.
That being said, I would assume that the majority of the chemical found in water comes from improper application (spraying before rainfall or irrigation, high winds, careless aerial application etc.) When applied following the label recommended rate, properly calibrated equipment, PPE and according to the local best management practices, there should be virtually zero risk of glyphosate contaminating water sources, or moving to off site targets.