From what I saw in a non-emulated video, an example of it was in this video:
https://youtu.be/wKBbwUtmmPY (Go to 5:34, the darkness of the video was actually from the user's capture card)
What Sega did to these 2D backgrounds to emulate fog effects is just cycling random colors to corresponding stages in the hardware itself rather than just making the whole background being photoshopped to white or darken the still backgrounds on the game's rom (Dural's Jeffrey stage which was showcased in that video), which Sega wanted to put Model 3 hardware to the test.