No. The mental model was exactly correct. Their assignment of notation to the model was non-standard when they wrote "+" for the operation of merging the wholes

No. The mental model was exactly correct. Their assignment of notation to the model was non-standard when they wrote "+" for the operation of merging the wholes. The confusion of what is wrong with what is correct but non-standard is in fact quite standard and quite wrong. The confusion of the mental model with the notation is also a standard mistake.