Halliday & Matthiessen (2014: 530-1):
The sky is about to fall. (i) – Who said that? (ii) – Who said so?
It is clear that both that and so stand for something that is projected, as shown by the verb said. In (i) this projected element is being treated as a quote: ‘who produced that verbal act?’ – hence we can ask who said that? if we want to identify a speaker from among a crowd, like a teacher finding out who was talking in class. In (ii), on the other hand, the expression the sky is about to fall is being treated not as anybody’s verbal act but as a text; the meaning is ‘who affirmed that that was the case?’, with the implication that the contrary is conceivable.
In ‘verbal’ process clauses, therefore, he said that simply attests his production of the wording, whereas he said so raises the issue of whether what he said is in fact the case.