It depends on what you mean by "Visualized Data."

Do decision makers use graphs, charts, dashboards, etc? Yes of course.

Are there some visualizations that wouldn't be of any value to a decision maker whatsoever? Also yes of course. You can't show me a word cloud if I work as a portfolio manager for a bank and expect me to make any decisions from it. That being said, the social media team might be able to. It all depends on the audience, and whether or not you're making patterns they care about easier to detect.

If you are talking about graphs/charts/dashboards, what I would do if I was in your shoes is I would try to make one dashboard with (say) 3-4 graphs inside of it, and then I'd show them that dashboard and say something like, "You know, I've been thinking about that conversation we had. And I definitely appreciate the point you made about fluff visualizations. But I also really think there's at least a few charts that would be really valuable to you. I whipped a few together (on my time, not yours!). Do you have a few minutes that you could spare to come have a look at them with me?"