Baswell - I think you did misread it - that paragraph 2 (7)(d)(vi) allows for the carriage of goods for purposes other than trade as a private op i.e flying your new TV home. I think you are reading it as carriage for trade excludes it from a private op, but that is allowed with conditions in the earlier paragraph.
The earlier paragraph (v) refers to carriage of goods for trade, provided the goods are owned by the pilot, owner or hirer of the aircraft (i.e not just flying random cargo) and that the pilot is not paid then it is a private op. Once you charge for the flight or the pilot gets paid it becomes airwork.
But of course if they used plain english we would have a lot of out of work lawyers.