[cdavidcash]

He is mistaken. What he meant is that there exists a finite field with exactly 256 elements, so you can "make" {0, ..., 255} into a finite field (in the sense that you can make any set of size 256 into a field by assigning + and * operations), but addition and multiplication in that field won't be the usual modular integer arithmetic. Instead, the operations will be determined by mapping the numbers to polynomials and performing modular polynomial operations and then mapping them back to numbers {0,...,255} (or determined by some other process that is morally equivalent).