I was able to use my CD on a PC, so it's Canon not updating the Mac version.
Since I was today (2/4/16) able to downgrade the firmware, I figured I would update the process:
1. On a PC, get the latest version of EOS Utility, or the one that came with your camera.
2. Turn off Live View on the 5d mkiii. For some reason, firmware update is grayed out in EOS Utility if LiveView is on.
3. Plug the mkiii into your computer via USB.
4. Launch EOS Utility.
5. Choose "Camera Settings / Remote Settings" from the menu
6. In the middle of the remote window that opens, choose the wrench button (just like in the video here:
7. Click on the firmware button now.
8. FOLLOW THE ONSCREEN INSTRUCTIONS VERY CAREFULLY AS THEY INVOLVE SWITCHING BACK AND FORTH BETWEEN THE REMOTE SCREEN OPEN ON YOUR PC AND THE DISPLAY ON THE BACK OF THE MKIII.
9. When it's finished updating, select OK and turn off the camera.
Note: After this finished, nothing happened when I turned the camera back on or off except for "sensor cleaning." No interface on the back of the camera for at least 6 tries to turn it on and off, and then it suddenly started working. I am not sure what caused this.