hey artfuldodger, love that name!!!, that is a good question that seems like many people have. Not much possted out there that gives a clear explanation on this. ORS_techhead did gather a pretty complete breakdown of Thule gear carrier compatibility with the Thule 376 commercial truck rack and all other van rack and truck racks in the Thule PRO series commercial truck racks. Basically, many of the Thule gear carriers need the Thule Xadapt adapter kits to connect to the bars.
His post is here...
Thule Xadapt / Thule Pro Series truck racks compatibility list