If your clips don't have brass inserts in them (so they'll fit on metric stands), then maybe you've got metric stands (which have a smaller threaded end on them)?
The brass inserts are removable from the clips with a large flat-blade screwdriver, or a U.S. "dime" ($0.10 coin).
What everybody is telling you about the adaptor is correct. The JM27SM shock mount comes with the brass adaptor already screwed in. Ala kid klash's post, stick a dime or flatblade screwdriver into the slot and twist lefty-loosey!