And when a company stores an item, it doesn't move along with the company, but that doesn't mean the item is never associated with the company.
CRF, Movement/Hazard Phase, emphasis added wrote:A company is considered to be at the site given by its site card at all times except from the moment their new site card is revealed during their movement/hazard phase until their old site card is discarded during the same movement/hazard phase.
MELE Movement Rules, emphasis added wrote:At the beginning of its movement/hazard phase, a moving company's current site card becomes its site of origin - the company is considered to be en route to its new site card (i.e., the company is moving).
At the end of a moving company's movement/hazard phase (before players return to their hand sizes), its site of origin is removed (discard if tapped; otherwise, return it to your location deck) and the new site card becomes the company's current site card.
All of these indicate that the site card is directly associated with the company. Whether another mechanism can disassociate them is irrelevant.