Nope, we are not saying the same thing. Daniel wants you to plane the whole sides to fit the curve. I want you to hang normal boxes in a lattice with a front that follows the curved sides only where the drawer front meets the sides. You can make the front from a single piece by doing half blinds into a rabbet or with an applied front on a straightforward through DT box. The latter would like make side runners easier to make too.
~ Do not seek to follow in the footsteps of the men of old; seek what they sought.