You're right to question the boiling. I was thinking of death by suffocation in heated steam. Boiling is not the technically correct term.

Here are some more sources that nearly all livestock live in factory farms: [Our World in Data, PETA,]; there are a lot more I can find searching the web but they mostly seem to link back to the Sentience Institute's research. OWiD's is based on SI's research, and I suspect PETA's claim is based off SI's as well. More importantly, I haven't found any claim that the proportion is lower than 90%, or even anyone challenging SI's figures. Do you have reason to doubt this? And if so, can you find any source? It seems plausible to me just based on the fact that factory farming is vastly more efficient than other methods, and most people aren't picky about such things. Just as a prior, I would expect that the vast majority of livestock are found in the most efficient types of farms.

Without any attempt to describe the methodology used for their estimates.

I mean they literally have their calculations available right there as an easily-viewable google sheets link. And the data source is clearly stated: "these estimates use the 2022 Census of Agriculture and EPA definitions of CAFOs to estimate the number of US farmed land vertebrates who are in CAFOs ("factory farms")."

You’d be trying to get that particular farm shut down, get laws passed to prevent that from happening. But you’re not doing that

Who is not doing that? Me specifically or animal rights people in general? I don't see why shutting down a particular farm would be very helpful, the scale of the problem is incredibly massive; passing laws would be much more effective. I would like to see laws passed, though, to stop these kinds of abuses. What would make you think I am not interested in that?