They are lying to you. The AARTO legislation has no reference to reporting of accidents.
You can read the entire act here.
While it is indeed a requirement to report an accident within 24 hours or on the first business day following the accident, and you can be prosecuted for not reporting the accident, it still does not give the SAPS the right to refuse to open a case and provide you with a case number.
An accident must only be reported within 24 hours if a person was killed or injured in the accident. However, if the report is made after 24 hours have passed, it does not mean that the SAPS can refuse to accept the report.
See this extract on the SAPS website. Section 61(1)(f) says the following:
if he or she has not already furnished the information referred to in paragraph (e) to a traffic officer at the scene of the accident, and unless he or she is incapable of doing so by reason of injuries sustained by him or her in the accident,as soon as is reasonably practicable, and in any case within 24 hours after the occurrence of such accident, report the accident to any police officer at a police station or at any office set aside by a competent authority for use by traffic officer, and there produce his or her driving licence and furnish his or her identity number and such information as is referred to in that paragraph; and
As you can see, there are certain reasons why the accident may be reported after 24 hours.