[math-fun] Borromean Rings

I thought it was kind of neat that Borromean rings cannot be formed using circular rings (of equal or differing sizes). A related question: Given three rigid rings which are not all circular and are reasonably smooth locally, is it always possible to form Borromean rings? I was inclined to think this was true, but then I thought it might not be possible if the rings were sufficiently tangled up that any attempt to form Borromean rings would result in a more complicated linkage. Is this question easier if we require the rings to be planar?