[dddd]

Something to keep in mind is that a narrower (typical with aluminum) rim not only flexes more in torsional deflection (that is the precurser to potato-chip failure mode), but that the narrower rim makes the tire more supple by altering both the shape of the contact area and the angle of the sidewalls meeting the rim.
Additionally, the reduced OD of the tire casing reduces casing tension at any given psi.
So all told, there are FOUR reasons why a (typically narrower) aluminum rim might make for a softer-feeling ride.

And it's not just the inside width of a carbon rim that contributes to a stiffer ride, since the outside width is usually greater yet due to thicker rim sidewalls, which presents the flexing tire casing with a wider area off of which the sidewalls must rest under larger localized tire deflections.

So I think that makes five reasons, which cumulatively may be significant, two of which (outside width and torsional stiffness) are to varying degrees independent of the exact inside width.