Actually you can requests loops/sites within the level that you're paying for--for example, the tent/popup sites have two loops, one being loop 2000 (Spanish Moss Lane) and another that I *think* is 1500--not sure on that one. Since you're paying for that level of site, you can (hypothetically) request, say, site 200 in loop 2000. You won't be guaranteed that site or loop, but they will make a notation of your choice.
The practicalities are first come first serve in most cases, but they are usually very accommodating if you check into the Fort as soon as possible. I usually ask for a site close to a bathroom because old age

and they've usually put us as close as possible. Once we were assigned a site that was kind of uh-uh for us, and since a nearby site was empty the Cast Members were fine with moving us there.
As anything, if they're really swamped with people streaming into the Fort to check in, your mileage may very.