An assembly is provided for an aircraft propulsion system. This assembly includes a center body, a scarfed inlet structure and an inlet passage. The scarfed inlet structure extends circumferentially about the center body. The inlet passage is radially between and formed by at least the center body and the scarfed inlet structure. A first component of the assembly is configured to rotate about an axis relative to a second component of the assembly between: (A) a first position where a metering portion of the inlet passage has a first area; and (B) a second position where the metering portion has a second area. The first component is one of the center body or the scarfed inlet structure, and the second component is the other one of the center body or the scarfed inlet structure.