After posting this note, I saw some things under "More Like This" and read all of them. This gave me an idea to remove all the delete relationships and confirm that the main record in the subsystem could itself and a few other things. That worked, so I started adding delete relationships back in. This allowed me to narrow down where the problem was coming from.
Then I realized that maybe my test cases for deleting need to have all the records that can be deleted before I try to delete it. Deleting something with no children doesn't challenge the condition that causes the error message. So now I'm going to go back and create test cases that have all the children I want to delete, so that I can see where the problem is really coming from.
(This note is now as much for myself as the rest of the community. If I find something, I'll post the solution here. It looks like this comes up from time to fime and isn't easily diagnosed.)
I've seen this message when one side of the relationship is a Global
> and have gotten this message when I try to delete some records, but not all