Eureka! I recently bought a 2012 Equinox, and it came with the crossbars.
I took them off with this no-tools method:
Slide the rear bar forward a few inches.
Behind where it was there are a pair of spring-loaded latches on the inside of the roof rail, at the front end of a short plastic panel.
Push the two latches backwards and pull them towards the center of the roof. They are part of a 6-inch or so long plastic panel that you can now pivot towards the car's centerline. Once it's pivoted slightly, you can pull it towards the front of the car and two tabs holding the back end in place will be free and you can remove the whole piece.
Do the same on the other side.
Slide the crossbars back all the way one at a time, and you can angle each bar so either end of the bar can be rotated out through where the plastic panel used to be.
Do that for both bars, then snap the plastic panels back in -- first put in the rear hooks, then push in the snaps at the front end.