You either keep the virus completely out, or suppress and control initial infections until you suppress it below the level that it can spread ( with 100% effective LD), or, you "flatten the curve" delay the spread and thus delay the progress towards herd immunity, or, you throw the doors open and "welcome Coronavirus, spread as fast as you can please" to hell with the consequences.
So where is SA?
We tried and succeeded in getting rid of imported cases with travel restrictions and quarantine. Then the virus got out and we claim we succeeded somewhat in flattering the curve. But like it or not, it is "out there" and it WILL spread unabated until we get to herd immunity, or a vaccine shows up to help us get there.
So, no, The govt might have tried to convince the population that the LD will stop the virus in its tracks but anyone with two brain cells could quickly see that what would happen is a slower, hopefully, controlled move towards herd immunity.