Yes we do but only if you own property in SC and pay property taxes on it.
Luke, if you open the non-resident form you'll see it's a Real Property Tax verification form.
The section of code is S.C. Code Section 23-31-215(A)(3)
(A) Notwithstanding any other provision of law, except subject to subsection (B) of this section, SLED must issue a permit, which is no larger than three and one-half inches by three inches in size, to carry a concealable weapon to a resident or qualified nonresident who is at least twenty-one years of age and who is not prohibited by state law from possessing the weapon upon submission of:
(3) proof of residence or if the person is a qualified nonresident, proof of ownership of real property in this State;
SC is notorious about being slow to update their sites.