There is no "assumption" as to how much land is used to produce animal feed, it's simply a measurement of acreage.
Assumption 1) The land is suitable for human crops. A lot of land used for grazing is not suitable;
Assumption 2) All plants produce the same amount of food per acre; Less productive, but more tasty food could require more acres;
All science is based on assumptions. If you don't know the assumptions you cannot assess the plausibility of the claims.
And yes there certain types of crops such as almonds that do require an inordinate amount of water, but they are few and far between, and if you want to play, you pay. But I don't think most vegetarians sit down to dinner to a plate full of almonds.
This is my point. You don't know how getting rid of meat would affect the mix of crops grown and you certainly can't make assumptions based on the patterns of willing vegetarians today. The mix of crops would reflect the tastes of many unwilling former meat eaters in need of protein. The environmental impact will be larger than the impact crops grown for animal feed. How much more depends on the assumptions.