This is correct, if hop just over the border you will get maximum 7 days to leave the country. 

Overstays of less than 30 days end in ban for 1 year and with more than 30 days day will make you a unwanted person for 5 years. Even if you applied for visa extension at home affairs. 
Since 26th Mai 2014 you can not apply for an extension for vistors visa in South Africa.