Ironically I just found it about 15 minutes ago, sort of. Turns out it's not any particular part, but rather something to do with the tune sheet menu in GE. I made some LSD changes there and came back to the game and I had all the tires for the car I just modified. While that may seem all fine and dandy, it really isn't. The result is pretty much the same as the "Enable All Tires" function on Luca's editor, meaning if you haven't installed dirt or snow tires on the car yet and you do this, it will not let you race on dirt or snow even though it says you have them, regardless if the car allows it or not.