You're misunderstanding the point I (and the author) make. It's not a problem that cold air gets replaced by warm air because that might heat up the milk in the

You're misunderstanding the point I (and the author) make. It's not a problem that cold air gets replaced by warm air because that might heat up the milk in the fridge (this is where thermal capacity of the fridge content would be relevant). It's an issue because the warm air needs to be cooled down to fridge temperature and that costs energy. So the relevant question is "how much of the total energy loss of the fridge is caused by cooling down warm air repeatedly after every opening)