It is an artificial situation, similar to the 'had had' one:
Two teachers are discussing a pupi's written work. The pupil had written this sentence:"He said was wrong."
Teacher A. The pupil should have written "He said that was wrong". (1)
Teacher B. To be formally correct, it he should have written, "He said that that was wrong". (2)
Teacher A: I feel that 'that that' is clumsy. (3)
Teacher B: Well, I feel that that 'that that' that I suggested is correct. (5)
Teacher C, on hearing of this conversation later: He said that? That that 'that that' that he had suggested was correct? I don't believe it! (6)
Student or Learner