Test groups are great for grouping test items that depend on each other for them to work. However if one of the test items in the group fails the entire group should fail and the test should move on ...
I think this would need to be a user configurable option. I'm not sure I would want this to be a default behavior. I'm also not sure groups were ever intended to be used in this way. It seems to me that the test items described, should probably be part of their own test, so that the whole test fails when a test item fails. I think groups are more for grouping test items for convenience of expanding/collapsing, copying/pasting, or enabling/disabling.