Ah, I misspoke -- I was originally handling dragging one object on top of another by sending a message to the drop target in OnDragMove. Then I realized that I was duplicating functionality that already existed in UICamera and switched it to use OnDragOver and OnDragOut. The actual problem was that I was still getting drag over and out notification even if I dragged along a restricted axis.
What I did not realize (until I looked at it just now) is that this is probably by design. The camera sends these without regard to UIDragDropItem settings, because I expect that this is useful in other areas (such as handling gestures).
Knowing that is the case, I did in fact wedge a flag in there, but as you recommended, it's in user code where it belongs.