Are ecological arguments for vegetarianism just nonsense?

Some vegetarians make statements about how it takes less energy to grow grain than to feed an animal, yet a look at most any third world country says this is nonsense. If you told Inner Mongolians to grow corn instead of eating sheep, they’d starve. Their rocky ground only supports sparse tufts of grass. However since sheep can harvest and process those tufts, Mongolians have mutton, milk and cheese, wool and leather, all of which help them survive. In Vietnam, a pig is fed on scraps not suitable for human consumption. In other countries, pigeons are housed and free to collect their own food of bugs and plant scraps in the wild.
All of these are long established and important food and animal product sources that are not being fed human-suitable grain. Midwest animal feed lots are the exception in the world, not the rule, so is there really a valid ecological argument about vegetarianism?