(My guess is that logical incoherence is a result of lobbying by clergy. But even if the Reverend encouraged it in his church, state law prohibits it.)
Because there is some confusion here, I looked up the relevant statute, which is SC Code Section 23-31-215(m)(8), the current version of which provides:
(M) A permit issued pursuant to this section does not authorize the permit holder to carry a concealable weapon into a:
(8) church or other established religious sanctuary unless express permission is given by the appropriate church official or governing body[.]
Thus, pastor Pinckney could have given CC permission, but didn't, probably because of his strong opposition to CC. That disarmed him and his flock and made then sitting ducks for the atrocity.