To answer the OP's question, the President CAN overrule any decision by the Secret Service, but as a practical matter the President follows their lead as they have the experience and institutional memory on what works and what does not.
If the USSS had their way, the President would never leave the White House, would never work a rope line, and certainly would never walk any part of the inaugural parade. I can assure you they were not happy with the surprise Iraq trip.
If the President were to somehow decide that he was going flying in a 172, the Secret Service could not stop him.
What makes the President comply with the USSS is his knowledge of the very real and serious threats to his life (which we never hear about), and the President's rational desire to remain alive.