That is correct. But I think you are dismissing culture too lightly. For the captain or PF to continue below minima while still not visual, shows implicitly that he worked in an organisation whose values - i.e. culture - permitted, (or encouraged, or tolerated, or turned a blind eye to, whatever.....) taking such such a decision. Often these kinds of operators are underfunded, small outfits for whom one go-around or missed connection can have a disproportionately large financial or public relations penalty.

In addition to the actions of the day, a pilot's decision to join or continue working for this kind of company is in itself part of the chain of error leading to the site of the accident. If he worked for an operator whose values were the opposite, e.g. descending below minima with no visual contact is a firing offence, then the chances are this incident wouldn't have happened.

Busting minima is always survivable. Until it isn't.