If there is a thing under a thingy, the user group that can "add" entries to this thing and "edit" entries of this thing have permission problems (go to the backend Edit/Add Thing --> Edit Screen page):

1. when a user is among the "who can add" group but not among the "who can edit" group, he can neither add entries to the thing nor edit existing entries of the thing;
2. when a user is not among the "who can add" group but is among the "who can edit" group, he can both add new entries to the thing and edit existing entries of the thing;
3. when a user is among both the groups, he can do both (the same result as 2).

So it seems as if the "who can add" group doesn't function, while the "who can edit" group functions exceedingly by taking over the "who can add" function.