I think you answered the question when you said it doesn't fit.
The person is entitled to counsel, so the person has his or her own counsel. Special advocates in immigration proceedings are used in situations when the state has security information it wishes to present before the court but the information is of such sensitive nature that it should not be disclosed to the individual or his or her counsel. That's why the special advocate there is a person who would hear the information and represent the interests and cross-examine information. However, in this situation, the state is not leading any evidence against the individual. It's very much a situation in which the person being investigated provides testimony and that person could have his or her own lawyer if he or she wished.