They used false names because they knew riding in S. Africa at that time was against the rules of the UCI and would make them ineligible for the 1976 Olympics. To suggest they were hiding their identity out of some sort of shame is just to apply modern attitudes to a time nearly forty years ago. It was a reporter covering the honeymoon of Elizabeth Taylor and Richard Burton who rumbled their deception so that will give you an idea of the attitudes where big film stars felt no shame in holidaying there.
They weren't taking a stance they were getting some Winter training in prior to the Olympics. This was an era of shamateurism in the Olympics and bending the rules wasn't seen as shameful, just levelling the 'playing field' with the East Europeans.