I think that the CBSA has presented things in a really confusing way. My initial reading was exactly the same as yours: here are the four points, follow them and you'll be fine. That may be the case for Canadian residents returning to Canada and using a TDC.

For other Nexus members, those who do not use a TDC when entering Canada in a Nexus lane, they are very clear that you need to be within your personal allowance. The four points indicate that third-party goods are not within your allowance, leading me to the conclusion that I, as a US resident, would not use the Nexus lane with third-party goods. It does seem like it would be OK for Canadian residents.