I'm not saying that culture doesn't exist but it exists in the decisions that are made by the people who run the companies themselves, they set the tone and precedent for how the company works and the employees take note and follow.
The decisions are important, yes. But the person at the top isn't making every decision. They may have the best intentions, but if somewhere down the chain of command someone is prioritizing the wrong thing, focusing on the wrong thing, but still doing their job okay, they won't be told to do differently or let go. Defining a focus allows their immediate superior to recognize they're not doing their job. It even allows their subordinate to tell the manager "Hey, our mission/values statement says X; are you sure we should be doing this?" and possibly fix it without escalating it (though if escalation is necessary, it also provides a reason to escalate it, and a reason for the superior to pay attention).
Corporate culture provides a framework for understanding why managers make the decisions they do, and for employees, peers, and the public to hold managers accountable for the decisions they make.
If your opinion is that the people who run companies have no constraints or influences on their decisions, I would strongly disagree with you. The Tylenol example shows the power of culture--it gave J&J leadership the license (but also the pressure) to set the correct priorities when making decisions on how to handle it.
There's a book called The Leadership Moment by Michael Useem that I really like. About half the stories in it pertain to corporate culture either positively (Merck) or negatively (Salomon Brothers).
A classic example of a difference in corporate culture (how employees contribute to quality) is illustrated by this story from This American Life: