Just reading the article you provided and
"Feeding high grain diets to cattle unequivocally lowers the formation of CH4 in the rumen."
seems to disagree with what you're saying?
That isolated statement only loosely connects to the over reaching statement which I responded to: the performance of the high grain diet depends on the type of grain. In addition, there are complications.
From same section of the article it was picked from :
"While increased use of grains in ruminant diets
reduces enteric CH4 emissions, there is concern that
increased grain production may increase the use of
fossil fuels for fertilizer, machinery, and transport,
resulting in more greenhouse gas emissions. Grain
feeding ignores the importance of ruminants in converting fibrous feeds, unsuitable for human consumption, to high-quality protein sources (i.e. milk and meat). Furthermore, high grain diets can negatively affect cow health due to acidosis. With escalating grain prices, the scope of further increasing the grain content of ruminant diets in Canada is limited"
Even ignoring CO2 cost, nutrition, grain availability and all other complications, what is required to show that grass fed diets necessarily lead to more methane output than alternatives - is a comprehensive study of the performance of all dietary options and supplements. I dont think that is setting too high a bar, to avoid arguing on sweeping generalization and loss of context.
As in, my typing is reasonably fast, but I don't think I need to practice programming-style typing to increase my productivity. The logic, design, and debugging is where my time is spent.