I was trying to add mates to a part that already had mates to a part that should have had a fixed position. After applying the mate, both parts swung way out of position.
The part that shouldn't have moved had a coincident origin with the assembly's origin. The part cannot be dragged normally. Is this a bug/oversight?
Add on top of that, annoyingly the thing rebuilt in the middle of the command (why the HELL does it do that!?!?) and then rebuilt again upon cancelling the command. That took an extra five minutes at least! Very frustrating that it does that.