I believe it would be Code compliant to run one underground branch circuit to a storage shed and install a duplex receptacle without driving a ground rod etc. The single branch circuit would of course include an equipment grounding conductor. Am I correct?

yes

Frank,
Don't forget that 225.31 requires a disconnect at the shed. The exception to 225.38 permits the use of a "snap" switch as the disconnect.
Don

Thank you for replies. I wasn't aware of the disconnect rule Don. A snap switch is certainly easy enough.