ID number required for an exchange

I received a pair of shorts as a gift for Christmas and went to exchange them on the 29/12. The tag was left on the shorts but I obviously didn't have a receipt as it was a gift. In the meantime the item was reduced by R100 which I accepted since I didn't have a receipt. I chose something else of a higher value to exchange. In order to do the exchange they wanted my ID number which I refused to provide as I have no account with the store and am concerned about them recording my ID on their system for an exchange. I offered to give the usual details every other retailers require like name, number etc but this was unacceptable. No store manager was available. I had to use my own phone to phone the customer service department whilst in the shop twice. They wouldn't help saying it was up to the store. The manager came back from lunch, phoned regional manager and they refuse to exchange an item without your ID number. The first thing you are taught with ***** prevention is not to provide your bank details and ID number. I do not know how well their systems are protected and do dot see why I need to provide an ID number to do an exchange. I was told I can't exchange the item and was told if I get the matter resolved at a later date and the item is further reduced then I will lose out more. I find this policy completely ridiculous and it puts the customer at risk, not to mention that the customer service provided was poor. I compromised as a customer, lost value and may lose further value which the store manager did not seem to care about. I asked for the name of the head of the Donna Claire group which the store manager did not even know.