I just tried to use the Cmd-click trick to select a group which was lower than something obscuring it. So, I thought, okay I'll just Cmd click and then click again to get to the group. Problem is, instead of selecting the group, it selected only one object inside that group.
This should work in levels. Cmd click once to let AI know what you're about to do, click again to select the next thing below. If that thing is a group then the group should be selected. Not something inside the group; that could be yet another click.
I wound up having to take my work apart in order to select something, and then move it all back into place.