What the council says is nonsense, but it's also up to you to prove the loading exemption with a clear and consistent account at the Notice to Owner stage.
We have a bit of time to put a strong representation together, so let's start with gathering all the facts.
Firstly make a list of the items: how many boxes, how heavy, what was in them (you don't need an itemised account, a general description like "books", "kitchenware" or whatever else is fine).
Secondly, make a map showing the exact path from the car to the premises.
Also explain any access issues: is it a basement, top floor flat, did you have to go through a communal entrance and so on.
We can then start putting a draft together.