I understand your concern. In view of the high rate of credit card fraud in South Africa, this is standard procedure for SAA (although not for - at least some - other airlines in South Africa). Why they also apply this rule for bookings made in less crime-infested countries is not quite clear to me, but that's the way it is. I have not heard about any problems with this (like the credit card details being abused), so I think the risk is low.
As said by others: if the CC owner is with you when you check in, he can show the card and that should be sufficient.
If going to an SAA office beforehand solves the problem, I am not sure: when I made a booking recently for an international trip and went to the ticket office here at CPT airport to colect a receipt, I: a) had to show my CC to the ticketing clerk there (an had to sign a CC slip 'for identification only') AND b) had to show the CC again to the check in agent a few days later.
All in all: they are quite stressed about this CC story (and probably have reason to be, unfortunately).