Wouldn't "Damit" imply a ... "So that I have nothing to do". I would have thought "I have nothing to do with that" would have been "darüber" since the later seems more like 'over that' or 'about that', no?
No, I think it's just an illustrative example of one of the many uses and constructions of damit, to show (or remind) us that it's not solely used to head subordinate clauses with the meaning "so that." Damit has other meanings and uses as well. :)