Halliday & Matthiessen (2014: 530):
There are different ways of referring back to what is quoted and what is reported. Typically a reference item, usually that, is used to pick up a quoted passage, while a substitute, so/not, is used with a report. For example,She said, ‘I can’t do it.’– Did she really say that?
She said she couldn’t do it.– Did she really say so?
This is because the act of quoting implies a prior referent, some actual occasion that can then be referred back to, whereas in reporting there is nothing but the reported text. This explains the difference in meaning between I don’t believe that ‘I do not accept that assertion as valid’ and I don’t believe so ‘in my opinion such is not the case’.