There are Gap Cover providers that do allow you to have a Gap Cover policy without Medical Aid. In this case they will use their own internal tariffs to calculate what a typical Medical Aid would have paid out for the treatment you received, and they will then pay you the balance, or excess, over and above that.
For most Gap Cover providers getting a Gap Cover policy without Medical Aid would be meaningless, in fact, most will not allow you to take out a Gap Cover policy without providing your Medical Aid membership number first.
Your Gap Cover is not a Medical Aid and will only pay shortfalls or gaps that your Medical Aid does not cover. Typically if your Medical Aid rejects a claim outright, your Gap Cover policy will also not pay anything because it only pays shortfalls, not an entire medical claim.