That's what I did. I used a 3/4" piece of plywood, cut to the dimension of the swivel rack. I glued and screwed it, also using small head trim screws through the side of the swivel rack, into the side of the plywood. That has worked perfectly for me.
When I tried to mount directly too the swivel rack, I couldn't get the screws to "bite in". It was like the back of the swivel rack was particle board, and the screws were just chewing out the material.