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.
The student was taking the model for ratios and applying it to fractions. If I need to add 2 + 2, and I multiply instead, I did the wrong calculation. It does not matter whether I multiplied correctly, nor does it matter that, in this case, both operations equal four.