What does "it’s the head of the fish that stinks" mean?

In a text regarding the meeting of the members of a automotive company appears:

In the past, there was one clear rule at our plant, I hope I’m not going to make anyone uncomfortable, but it’s the head of the fish that stinks. If we want to really make sure that safety becomes a priority, everyone needs to be aware of it, including middle management, but also the cleaning staff.

I have found a similar saying: the fish stinks first at the head. This means that "if the servant is disorderly, it is because the master is so" - see www.phrases.org.uk

Do you think that it’s the head of the fish that stinks also means that? Or does it have another meaning in that context?

Solution 1:

Yes, the expression is a variant of the one cited by the Phrase Finder.

They are saying that safety rules must be observed by everyone in the company, starting from the management level, down to the cleaning staff.

If managers (metaphorically the head of the fish) fail to do this, you can’t blame those in a lower position for not observing the rules.

Solution 2:

(The) fish rots from the head down, as per theidioms.com, states that:

It refers to failing organizations and how the blame of it should be
on its ‘head’ = the leadership. (It does not talk about the biology of the fishes)

The above definition leads me to believe that your assumption is indeed correct.

Solution 3:

In hot, humid tropical islands where unsalted catch go bad easily, the freshness of fish is commonly determined by its color and looks. When the color and looks are questionable, buyers usually resort to smelling the head.

Why the head? The head and internal organs putrefy faster than the flesh. But the internal organs lay deep inside the stomach where the smell is not readily detectable. The smell of the head is the easier measure. Thus the fish mongers’ saying, “the fish rots from the head down”. It’s a leadership/management idiom based from biological facts and experience.