Paul,
Go to the REST services directory, navigate to the service and then to the layer in question, and see if the Shape field is in there. Maybe the Shape field was not selected in the .mxd file and that's why you can get geometry back, and run spatial queries.
If it is, try running a query in there to see what results you will get.
If it is not in there, open the .mxd file, open the properties of the event layer, go to the Fields tab, and check the shape field. Save the document, restart the service, clear the REST cache, and try again.
Good Luck!