Unfortunately, this did happen today

This is the "collection" counter at the Home Affairs branch in Cape Town at 8:15 am. The office opens at 7:30 am, and my compatriots and I queued on the sidewalk at 6:30 in the predawn rain just to get near this set of desks, but at this point no one had even made an appearance. Once our presence was acknowledged (I had to come here to receive the stamp in my passport after delivering my application a minimum of 10 days ago, the Turkish man next to me was trying to obtain a residence permit so his family will be able to immigrate to SA) it took almost two more hours for the stamp-staple-see-ya. Thank goodness for Zunes, snacks, and friendly boon-seeking companions.

And if you ever want to come to SA for longer than 3 months, for any purpose, get detailed advice from someone who's been through the process before, and start the process months earlier than you would with a 1st world bureaucracy (no offense, Jacob!).