My understanding is indeed, a fatter tyre has a lower RR, all else being equal (esp. pressure).

For the same pressure (and therefore same contact patch area), the material of a skinny tyre has to distort more when it rolls into the contact patch than that of a fat tyre. This material flexing is the cause of rolling resistance.

But often all else can't be kept equal. Fatter tyres can't take higher pressures without a thicker carcass, which increases rolling resistance. Usually high pressure wins.