A person by the name of Dr Dave made the following calculation on snopes to show the entire world population could be fit into the state of Texas, having 1000 square foot per person. So space is not the issue. But if food is the issue, you have all the remaining land in the world outside of Texas to grow that food. So what really is the issue? Power and control, perhaps, for the elite few who fear the masses.
I don't know anything about the claim, but I will do the math for you. Using the square milage you gave for Texas: 1 square mile = 5280 x 5280 square feet = 27,878,400 square feet. So 268,581 square miles = 7,487,608,550,400. For simplicity say 7.5 x 10^12. That divided by 7 x 10^9 is indeed over 1000 square feet per person. So if we made one giant one-story compound over Texas, land, water, and all, we would each get a 1,000 square foot unit.