Theres only one thing you can do to fix this, realign the skinmesh with the car wheel, my guess is thats the issue.
To align it properly first uncheck the skinmesh from the car wheel ( disconnect the 2 in the list editor), be sure to show the car wheels, shift right click the wheel to locate its center, then use the menu > Edit > move object to cursor (aligned), then click on the skinmesh. then connect the skinmesh to the car object in the list editor, this is the same process for all wheels and on both the car and pcar objects.
the issue here is he is not using car or pcar objects, but a custom wheel object with a custom texture so having a separate wheel rigid/skin may not be relevant. [edit: the wheel's 'display geometry' option would be used to show his custom texture]
if the left wheel is fine then need to copy it's settings relative to the right wheel, by moving the car to world centre loc/rot XYZ=0,0,0 and 0,0,0 and comparing the L+/R- wheel values. also should check the wheel is not colliding with the car rigid body when turning by hiding car skin/showing it's rigid.