I am afraid the explanation in the manual might be a bit short.
All Radio buttons which are created subsequently, without pressing any other buttons in between, will be put into a group. I don’t think it is possible to modify any groups after they were created.
Spade, you didn’t overlook anything…I had the same issue and found that you will need to right-click go into properties and name the radio buttons under “Type” the same name to group them