The fender has an 'L' shape to it for reinforcemnet purposes. This "lip" rubs against the tire if the offset of the rib is off a bit or the tire is too wide.
What people do it "roll" this lip. They bend the lip up sacrafising some rigidity in the fender but not much. The method used to roll it most popular is to get a wooden baseball bat, jack the car up and run the bat over the lip using the tire as a guide slowly bending it as to not crack the paint. Heating it is also recommended.
Professionals have a tool that mounts to your wheel hub and works the same was as the bat method.
It takes some patience and it's definitely not for the weak of heart. As was mentioned, it's recommended to heat the paint around the fender first with a blow dryer to make the paint more pliable and cause less chipping.