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Separating Axis

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I've coded up an intersection test for convex polyhedrons, more specifically OOBs using the separating-axis thereom. It seems to work fine, at least for the test cases I've tried it with. Now I'm working on detection of the actual collision between the boxes, basically plane vs vertex and edge vs edge plus degenerate cases. However, while doing this I began thinking more on the separating axis thereom for intersection tests. If two convex polyhedrons are disjoint, then there exists a projection along an axis orthogonal to a face or orthognal to an edge in each polyhedron where they are also disjoint. I can't for the life of me visualize any case for 2 OOBs where they would be disjoint and NOT have a separating axis based on faces. In otherwords, is the 2nd part of the thereom necessary? Can someone give me a case where projections on the faces all overlap but the polys are disjoint?

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