My conclusions is that GHG from cattle is simply not as big of a deal as the environmentalists would make it seem. Another comment mentions that decaying grass also releases methane so I'm not even sure if there are any accurate numbers on the true effect of livestock on emissions.
All plants eventually decompose, but it happens at a much slower cycle than if we actively harvest it, feed it as grain, grow more where the original harvest was, etc. By speeding up the cycle, we end up with much more of it. Or at least that's my non-scientist take.
We gotta remember that "greenhouse gases" aren't a bad thing. They're fundamental to making Earth hospitable for life. But there's a balance. When we speed up the "carbon cycle", we end up with too much of the stuff, which throws the whole system out of balance. But we could just as easily end up with too little some day in the future, which would cause us all sorts of other problems.
As for whether we have truly accurate numbers for any of this, I too am skeptical. But it's early days for research in this area. One or two studies doesn't cut it, but that doesn't mean they're not onto something huge.