Yes, there is an implicit symmetry. Think of it like a full neighbor list vs a half neighbor list. If you use a full neighbor list, each pair-wise interaction is counted twice, and you have multiply the result by a factor of 0.5, but not if you use a half-neighbor list. The same is true here. If you use the full sphere of kspace vectors, you have to multiply the result by a factor of 0.5, but not if you use the half-sphere.
To get the half-sphere, all the negative kx terms are eliminated, along with the negative ky terms at kx = 0, and the negative kz terms at kx = ky = 0. So if you include all these eliminated terms then you could get the full sphere.