I have access to a database of over 30 million id numbers. Do you trust me with your information? Home affairs do - they sold it to the company I get the access from.
I'm not saying identity theft is not a real problem in SA [and indeed all over the world]. I understand people's concerns about giving out their ID numbers - especially to "new" websites, etc. However, as the ID Number is the only form of validation as to who someone is in South Africa, it is also understandable that companies need to protect themselves from fraud by verifying ID Numbers etc. Don't just give your ID Number to anyone, but remember, just as much as you may mistrust others, companies have the same right to mistrust you until you've proven who you are as well as your intentions.