How can an aircraft’s maximum design operating speed be greater than its never-exceed speed?
Maximum design operating speed means "we calculated the aircraft will break apart at that speed". It's obviously higher than the never-exceed speed, which means "you can safely operate the aircraft up to that speed".

Key here is the word "design". It always means something along the lines of "we calculated it to break at that load, please never try". The quotient of design load and maximum expected/allowed load is called safety factor. In this case, the safety factor is 1.1.