I would argue that it is a stretch of code definitions to interpret the face of a paper towel dispenser to be considered a 'wall or partition'.

I would add that the California text does not specifically require a 'clearance' related to that 18" that we would theoretically be obligated to keep clear.

Personally, I think that interpretation, while well-meaning, isn't supported in code.

11B-606.6 Adjacent side wall or partition. Lavatories, when located adjacent to a side wall or partition, shall be a minimum of 18 inches (457 mm) to the centerline of the fixture.

I agree with Bill Zelmer's comments, and don't know how one could interpret this as requiring the 18" to be clear of any objects, especially objects (soap and paper towel dispensers) associated with the use of the lavatory. Were the CBC requirement instead made a part of 11B-606.2 (Clear Floor Space), I suppose we'd have to give the notion of "clear" some more thought.

The question is where is the location of dispenser/element in question.

11B-606.6 requires lavatories adjacent to sidewall or partition to be a minimum of 18" to the centerline of the fixture without reference to dispensers or similar elements (as commented previously).

11B-606.2 requires clear floor space complying with 11B-305. Clear Floor Space is defined as the minimum unobstructed floor or ground space required to accommodate a single, stationary wheelchair and occupant.  Dispensers or other similar elements creating an obstruction or could be classified as a protruding object would have to be relocated.