I was curious about this as well, and also confused by the reference to rye "fixing" nitrogen. While checking on whether rye fixes nitrogen, I found this:

"If allowed to grow to maturity, rye residues tend to have a high carbon to nitrogen ratio and high percentages of lignin and cellulose, so they can be slow to decompose.

"Excessive amounts of spring residue produced by rye can delay cash crop planting and actually decrease the availability of N to subsequent crops as N is tied up or ‘immobilized’ by the decomposing residues. To avoid these problems, and to avoid ‘grow-back’ of the rye, it is best to thoroughly incorporate it when it is between 12 and 18 inches tall and still relatively succulent."
https://www.uvm.edu/vtvegandberry/factsheets/winterrye.html

So basically, rye still has similar environmental benefits whether harvested for grain or killed while still green, but the green manure benefits for the next crop are much higher with the latter. Which means that if there's not much demand for rye but there's a lot of demand for your next crop, you're going to grow based on what benefits your next crop, and not focus on harvesting rye.

And rye does not "fix" nitrogen--a technical term which means taking it from the atmosphere and converting it to a form that plants can use. (Beans and soil bacteria acting symbiotically do this.) And nitrogen fixing would not help with nitrogen runoff. I think the author didn't realize that there was a difference between "fixing" nitrogen and "immobilizing" nitrogen. From the same link:

"Rye has a good ability to scavenge residual soil N when it follows other crops, and it is commonly grown for this purpose. This reduces the potential for nitrate leaching into groundwater and it conserves N fertilizer inputs, which saves money."

• Reply