Yes, but this is true regardless of the irreducible polynomial used to form the field. My question is why that specific polynomial was chosen; was it an arbitrary choice or was there some reason?
"That first one that worked (100011011) is the one used in AES"
i.e., the polynomial that was chosen for AES (x^8 + x^4 + x^3 + x + 1) is the minimal irreducible polynomial of degree 8 (minimal in the sense of the natural ordering of polynomials). I guess that could be a good reason (but I'm not sure it's _the_ reason).