Yes, I thought that would be your argument but I thought it might help you visualise that there doesn't need to a be a couple to produce a rotation, just a force acting at a distance from the c of g.
I think we have got to the point where you either believe this is true or continue to convince yourself that opposing couples is the answer - I have run out of analogies to try and illustrate the point.
Maybe one more - imagine a helicopter hovering facing North (no wind, perfect hover), now attach a rope to the nose and pull from a position directly East of the helicopter. First the helicopter will rotate to point East and then (if you are strong enough) translate on an Easterly heading.
Why? Because the initial application of the force was offset from the C of g and produced a rotation - once the force was aligned with the c of g, the rotation stopped and the translation began (no moment arm).
Again, no couple, just one force acting about the c of g.