OK... some more info.
I tried it with 'Set Animation Speed' and it didn't work. But if I use 'Animation Settings' and try the speed setting there with -1... it does work. It plays the animation backwards over and over.
But here's where that gets flaky. Since it was playing the animation backwards over and over... I wanted it to NOT loop. So I went back into the 'Animation Settings' and tried to set the Wrap Mode to 'Once'. The pulldown will not let me choose 'Once'. Each time I pick 'Once', it injects 'Clamp' into the slot. Then I tried choosing 'Default', which I would have thought would default to whatever the animation clip was set to do natively. But when 'Default' is active, the cube never moves from it's frame1 position.
So it can be made to play backwards, but not without looping over and over.