I'm proposing closing this with reference to http://bugs.python.org/issue22047 

That focuses on the issue of adding mutually exclusive group to another exclusive group, but adding Argument Group has the same problems.

Solutions, short of the big http://bugs.python.org/issue11588 fix, include code that raises an error the user attempts to nest groups and/or adding a documentation note that nesting does not work.

There is one kind of nesting that does work - a mutually exclusive group can be nested inside an Argument Group.  The effect is to give the mutually exclusive group a title and help line grouping.