I noticed that in the newest version (was it G?) when you enter the pits (shift+p) the game automatically changes to the skin you had last (before the one you currently have) and it stays when you join track. If you go shift+p again, the skin changes back to the one you selected in the menu. The replay is of no use here since you can't see the garage screen.

So, if you want to try to reproduce it:
1. select a driver and a skin, leave pits
2. change driver and skin
3. leave pits (now you should have the skin you wanted to have)
4. enter pits again (the game should now automatically select the skin from step 1)
5. join track, you should now have skin from step 1 (even though you didn't select it)
6. pit again (you should now have skin from step 2)

E: It doesn't seem to work sometimes, but I think there is an issue with the game selecting the last skin used by a certain driver.