Absolutely they can.
In fact, this is the case in most businesses where we get called to assist with an accident investigation. These are not SAFTENG clients, but rather a 1-off project to lead the investigation with a referral from a safety agency or a friend of a friend of a friend kind of arrangement. We used to do dozens of these investigations each year, so yes, we saw a lot of major companies with their proverbial “pants down.”
But there is an argument that safety can not have its own culture and is just part of the organizational culture within a business, division, or facility. The theory is if the business/facility is terrible at production, cost control, and quality, it will also struggle with safety.
I have to come to realize that is really naive thinking.