The initial assumption was 40 missions a year. Based on the estimated risks you might get 100 missions from a shuttle on average. So 5 orbitors * 100 / 40 = 12.5 years or ~ 10 years with an early loss. They where in service for 30 years and averaged 4.5 missions per year.

For comparison compare the matence cycle a low mileage 0 to 10 year old car vs a low mileage 15 to 30 year old car.

I've heard this reasoning before (from NASA personnel), but I have never seen the reasoning behind it. Many of the design life requirements were impossible to meet to begin with, such as the 50-launch design life of the Space Shuttle main engines (because of the high chamber pressures, and problems with bearings). If you have some evidence of the veracity of this claim, I would be very interested to read it.

I wonder if that was "We believe they are capable of 100 missions, because we require 100 missions" or "We believe they are capable of 100 missions, because that is what our test data actually suggests".

See: Feynman's Appendix F. Specifically his criticism of the Shuttle reliability numbers quoted by NASA management and how they differed from the reliability numbers quoted by NASA engineers.

Design life and rated life (as built) are two completely different things. The Space Shuttle requirements stated that it should be capable of 100 missions, but I have never seen any document describing what they were rated for, after they were constructed, and the flight tests were completed.