both of those are 20 years out of date but I'll look at the methodology. it still seems off by orders of magnitude

the USGS paper says almost no water goes to livestock

Combined withdrawals for livestock and aquaculture were less than 3 percent of the total water withdrawals in 2005. Livestock withdrawals include water for livestock, feedlots, and dairy operations, and accounted for 2,140 Mgal/d, most of which (60 percent) was supplied by groundwater.

here's the relevant section from the pimentel paper

Water use in livestock production. The production of animal protein requires significantly more water than the production of plant protein (Pimentel et al. 2004). Although US livestock directly uses only 2% of the total water used in agriculture (Solley et al. 1998), the indirect water inputs for livestock pro- duction are substantial because of the water required for forage and grain crops. Each year, a total of 253 million t grain are fed to US livestock, requiring a total of about 25 × 1013 L water (Pimentel et al. 2004). Worldwide grain production specifically for livestock requires nearly three times the amount of grain that is fed to US livestock and three times the amount of water used in the United States to produce grain feed (Pimentel et al. 2004).

Animal products vary in the amounts of water required for their production (table 2). For example, producing 1 kg chicken requires 3500 L water, whereas producing 1 kg sheep (fed on 21 kg grain and 30 kg forage) requires approximately 51,000 L water (table 2; USDA 2003, Pimentel et al. 2004). If cattle are raised on open rangeland and not in confined feed- lot production, 120 to 200 kg forage are required to produce 1 kg beef. This amount of forage requires 120,000 to 200,000 L water per kg (Pimentel et al. 2004), or a minimum of 200 mm rainfall per year (Pimentel et al. 2004).

Agricultural production in the United States is projected to expand to meet the increased food needs of the US pop- ulation, which is expected to double in the next 70 years (USBC 2003). Developing countries are expected to feel the impacts of this food crisis to a greater extent as demands ap- proach those of developed countries and populations continue to rise (Rosegrant et al. 2002). Increasing crop yields neces- sitate a parallel increase in the use of fresh water in agricul- ture. Therefore, increased crop and livestock production during the next 5 to 7 decades will significantly increase the demand on all water resources, especially in the western, southern, and central United States (USDA 2003) and in many regions of the world with low rainfall.

so it looks like the methodology isn't even explicit in this paper, and we need to see pimentel's OTHER 2004 publication to understand how he arrived at the water values. MY SUSPICION is that he includes the water used in, for instance, cotton production to add to the sum used in livestock. that's at best an oversight: that "use" is actually a conservation of resources. given that i do see soy mentioned, i would also guess that it's including the waste product from soybean oil production, which accounts for 85% of the global crop weight but only 17% of the end use weight. the remaining ~68% of the global crop weight would be waste if not fed to livestock.

i can dig into the further methodology after work, but you should be dubious about these claims, especially the original source, which seems to be intentionally misrepresenting the USGS paper.